Direct and semidirect products in GAP [closed]
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Can someone please tell me the necessary codes/commands to enter the below group in GAP.
Thanks a lot in advance.
group-theory finite-groups gap
asked Aug 28 at 12:52
Buddhini Angelika
485
closed as off-topic by José Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt Aug 28 at 16:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." РJos̩ Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt
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up vote
0
down vote
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Can someone please tell me the necessary codes/commands to enter the below group in GAP.
Thanks a lot in advance.
group-theory finite-groups gap
asked Aug 28 at 12:52
Buddhini Angelika
485
closed as off-topic by José Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt Aug 28 at 16:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." РJos̩ Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt
1
Your question is ambiguous - you need to give the action of $mathbbZ_3$. For example, it may act trivially on one of the $mathbbZ_7$-factors, but not the other.
– user1729
Aug 28 at 14:35
2
Also, this question is pretty "low-effort" on your part - why can't you just google it? (In fact, I just googled it and found a worked example in the GAP documentation: gap-system.org/Manuals/doc/ref/chap49_mj.html)
– user1729
Aug 28 at 14:37
I tried according to the information in that link, but at the stage I'm trying to enter AutomorphismGroup() command I'm getting an error saying no method found. That's why I asked... Please help now, I have edited the question by including the description of the group.
– Buddhini Angelika
Aug 28 at 16:17
2
I suggest to edit your question to show what exactly you have tried in GAP. We need to see the actual code and the no-method-found message to suggest something. This will also place the question into the reopening queue. Do not post screenshots of GAP, as they are not usable - you need to copy and paste the text from the terminal and indent it by 4 spaces (e.g. like in the answer below).
– Alexander Konovalov
Aug 28 at 20:24
1
If you can describe the action of $Z_3$ through a $2times 2$ matrix overGF(7), e.g.m:=DiagonalMat([2,4]*One(GF(7)));, you could use the matrix versionSemidirectProduct(Group(m),GF(7)^2);.
– ahulpke
Aug 29 at 2:53
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up vote
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down vote
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up vote
0
down vote
favorite
Can someone please tell me the necessary codes/commands to enter the below group in GAP.
Thanks a lot in advance.
group-theory finite-groups gap
asked Aug 28 at 12:52
Buddhini Angelika
485
Can someone please tell me the necessary codes/commands to enter the below group in GAP.
Thanks a lot in advance.
group-theory finite-groups gap
asked Aug 28 at 12:52
Buddhini Angelika
485
edited Aug 28 at 16:15
asked Aug 28 at 12:52
Buddhini Angelika
485
asked Aug 28 at 12:52
Buddhini Angelika
485
asked Aug 28 at 12:52
Buddhini Angelika
485
485
closed as off-topic by José Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt Aug 28 at 16:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." РJos̩ Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt
closed as off-topic by José Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt Aug 28 at 16:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is not about mathematics, within the scope defined in the help center." РJos̩ Carlos Santos, Chris Custer, Alan Wang, Morgan Rodgers, Derek Holt
1
Your question is ambiguous - you need to give the action of $mathbbZ_3$. For example, it may act trivially on one of the $mathbbZ_7$-factors, but not the other.
– user1729
Aug 28 at 14:35
2
Also, this question is pretty "low-effort" on your part - why can't you just google it? (In fact, I just googled it and found a worked example in the GAP documentation: gap-system.org/Manuals/doc/ref/chap49_mj.html)
– user1729
Aug 28 at 14:37
I tried according to the information in that link, but at the stage I'm trying to enter AutomorphismGroup() command I'm getting an error saying no method found. That's why I asked... Please help now, I have edited the question by including the description of the group.
– Buddhini Angelika
Aug 28 at 16:17
2
I suggest to edit your question to show what exactly you have tried in GAP. We need to see the actual code and the no-method-found message to suggest something. This will also place the question into the reopening queue. Do not post screenshots of GAP, as they are not usable - you need to copy and paste the text from the terminal and indent it by 4 spaces (e.g. like in the answer below).
– Alexander Konovalov
Aug 28 at 20:24
1
If you can describe the action of $Z_3$ through a $2times 2$ matrix overGF(7), e.g.m:=DiagonalMat([2,4]*One(GF(7)));, you could use the matrix versionSemidirectProduct(Group(m),GF(7)^2);.
– ahulpke
Aug 29 at 2:53
add a comment |Â
1
Your question is ambiguous - you need to give the action of $mathbbZ_3$. For example, it may act trivially on one of the $mathbbZ_7$-factors, but not the other.
– user1729
Aug 28 at 14:35
2
Also, this question is pretty "low-effort" on your part - why can't you just google it? (In fact, I just googled it and found a worked example in the GAP documentation: gap-system.org/Manuals/doc/ref/chap49_mj.html)
– user1729
Aug 28 at 14:37
I tried according to the information in that link, but at the stage I'm trying to enter AutomorphismGroup() command I'm getting an error saying no method found. That's why I asked... Please help now, I have edited the question by including the description of the group.
– Buddhini Angelika
Aug 28 at 16:17
2
I suggest to edit your question to show what exactly you have tried in GAP. We need to see the actual code and the no-method-found message to suggest something. This will also place the question into the reopening queue. Do not post screenshots of GAP, as they are not usable - you need to copy and paste the text from the terminal and indent it by 4 spaces (e.g. like in the answer below).
– Alexander Konovalov
Aug 28 at 20:24
1
If you can describe the action of $Z_3$ through a $2times 2$ matrix overGF(7), e.g.m:=DiagonalMat([2,4]*One(GF(7)));, you could use the matrix versionSemidirectProduct(Group(m),GF(7)^2);.
– ahulpke
Aug 29 at 2:53
1
1
Your question is ambiguous - you need to give the action of $mathbbZ_3$. For example, it may act trivially on one of the $mathbbZ_7$-factors, but not the other.
– user1729
Aug 28 at 14:35
Your question is ambiguous - you need to give the action of $mathbbZ_3$. For example, it may act trivially on one of the $mathbbZ_7$-factors, but not the other.
– user1729
Aug 28 at 14:35
2
2
Also, this question is pretty "low-effort" on your part - why can't you just google it? (In fact, I just googled it and found a worked example in the GAP documentation: gap-system.org/Manuals/doc/ref/chap49_mj.html)
– user1729
Aug 28 at 14:37
Also, this question is pretty "low-effort" on your part - why can't you just google it? (In fact, I just googled it and found a worked example in the GAP documentation: gap-system.org/Manuals/doc/ref/chap49_mj.html)
– user1729
Aug 28 at 14:37
I tried according to the information in that link, but at the stage I'm trying to enter AutomorphismGroup() command I'm getting an error saying no method found. That's why I asked... Please help now, I have edited the question by including the description of the group.
– Buddhini Angelika
Aug 28 at 16:17
I tried according to the information in that link, but at the stage I'm trying to enter AutomorphismGroup() command I'm getting an error saying no method found. That's why I asked... Please help now, I have edited the question by including the description of the group.
– Buddhini Angelika
Aug 28 at 16:17
2
2
I suggest to edit your question to show what exactly you have tried in GAP. We need to see the actual code and the no-method-found message to suggest something. This will also place the question into the reopening queue. Do not post screenshots of GAP, as they are not usable - you need to copy and paste the text from the terminal and indent it by 4 spaces (e.g. like in the answer below).
– Alexander Konovalov
Aug 28 at 20:24
I suggest to edit your question to show what exactly you have tried in GAP. We need to see the actual code and the no-method-found message to suggest something. This will also place the question into the reopening queue. Do not post screenshots of GAP, as they are not usable - you need to copy and paste the text from the terminal and indent it by 4 spaces (e.g. like in the answer below).
– Alexander Konovalov
Aug 28 at 20:24
1
1
If you can describe the action of $Z_3$ through a $2times 2$ matrix over
GF(7), e.g. m:=DiagonalMat([2,4]*One(GF(7)));, you could use the matrix version SemidirectProduct(Group(m),GF(7)^2);.– ahulpke
Aug 29 at 2:53
If you can describe the action of $Z_3$ through a $2times 2$ matrix over
GF(7), e.g. m:=DiagonalMat([2,4]*One(GF(7)));, you could use the matrix version SemidirectProduct(Group(m),GF(7)^2);.– ahulpke
Aug 29 at 2:53
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1 Answer
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For things like this, I like to work with generators and relators, because then it's easy for me to be very clear about what the automorphisms are doing to the normal subgroup:
> f := FreeGroup("x", "y", "z");
> AssignGeneratorVariables(f);
> relations := "x^7=y^7=1, [x,y]=1, z^3=1, x^z=foo, y^z=bar";
> r := ParseRelators([x,y,z], relations);
> g := f/r;
Here foo and bar are the expressions in x and y that determine your action.
Of course, this gets more tedious when your base groups aren't abelian, but for this kind of group, it's not too bad.
answered Aug 28 at 15:29
Steve D
2,6371620
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
@BuddhiniAngelika: Once you pick $i$, you would writex^iinstead offoo, andy^(blah)instead ofbar. You need to figure out what $i$ is, and also what $i^t=$blah is.
– Steve D
Aug 28 at 16:30
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
For things like this, I like to work with generators and relators, because then it's easy for me to be very clear about what the automorphisms are doing to the normal subgroup:
> f := FreeGroup("x", "y", "z");
> AssignGeneratorVariables(f);
> relations := "x^7=y^7=1, [x,y]=1, z^3=1, x^z=foo, y^z=bar";
> r := ParseRelators([x,y,z], relations);
> g := f/r;
Here foo and bar are the expressions in x and y that determine your action.
Of course, this gets more tedious when your base groups aren't abelian, but for this kind of group, it's not too bad.
answered Aug 28 at 15:29
Steve D
2,6371620
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
@BuddhiniAngelika: Once you pick $i$, you would writex^iinstead offoo, andy^(blah)instead ofbar. You need to figure out what $i$ is, and also what $i^t=$blah is.
– Steve D
Aug 28 at 16:30
add a comment |Â
up vote
2
down vote
For things like this, I like to work with generators and relators, because then it's easy for me to be very clear about what the automorphisms are doing to the normal subgroup:
> f := FreeGroup("x", "y", "z");
> AssignGeneratorVariables(f);
> relations := "x^7=y^7=1, [x,y]=1, z^3=1, x^z=foo, y^z=bar";
> r := ParseRelators([x,y,z], relations);
> g := f/r;
Here foo and bar are the expressions in x and y that determine your action.
Of course, this gets more tedious when your base groups aren't abelian, but for this kind of group, it's not too bad.
answered Aug 28 at 15:29
Steve D
2,6371620
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
@BuddhiniAngelika: Once you pick $i$, you would writex^iinstead offoo, andy^(blah)instead ofbar. You need to figure out what $i$ is, and also what $i^t=$blah is.
– Steve D
Aug 28 at 16:30
add a comment |Â
up vote
2
down vote
up vote
2
down vote
For things like this, I like to work with generators and relators, because then it's easy for me to be very clear about what the automorphisms are doing to the normal subgroup:
> f := FreeGroup("x", "y", "z");
> AssignGeneratorVariables(f);
> relations := "x^7=y^7=1, [x,y]=1, z^3=1, x^z=foo, y^z=bar";
> r := ParseRelators([x,y,z], relations);
> g := f/r;
Here foo and bar are the expressions in x and y that determine your action.
Of course, this gets more tedious when your base groups aren't abelian, but for this kind of group, it's not too bad.
answered Aug 28 at 15:29
Steve D
2,6371620
For things like this, I like to work with generators and relators, because then it's easy for me to be very clear about what the automorphisms are doing to the normal subgroup:
> f := FreeGroup("x", "y", "z");
> AssignGeneratorVariables(f);
> relations := "x^7=y^7=1, [x,y]=1, z^3=1, x^z=foo, y^z=bar";
> r := ParseRelators([x,y,z], relations);
> g := f/r;
Here foo and bar are the expressions in x and y that determine your action.
Of course, this gets more tedious when your base groups aren't abelian, but for this kind of group, it's not too bad.
answered Aug 28 at 15:29
Steve D
2,6371620
answered Aug 28 at 15:29
Steve D
2,6371620
answered Aug 28 at 15:29
Steve D
2,6371620
answered Aug 28 at 15:29
Steve D
2,6371620
2,6371620
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
@BuddhiniAngelika: Once you pick $i$, you would writex^iinstead offoo, andy^(blah)instead ofbar. You need to figure out what $i$ is, and also what $i^t=$blah is.
– Steve D
Aug 28 at 16:30
add a comment |Â
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
@BuddhiniAngelika: Once you pick $i$, you would writex^iinstead offoo, andy^(blah)instead ofbar. You need to figure out what $i$ is, and also what $i^t=$blah is.
– Steve D
Aug 28 at 16:30
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
Can you please tell how to write the relations according to the edited group information present in the question. I tried according to my knowledge but it fails. I'm bit new with the semidirect product, but I need to enter this group in GAP for one of my computations. Please help. Thanks in advance.
– Buddhini Angelika
Aug 28 at 16:20
@BuddhiniAngelika: Once you pick $i$, you would write
x^i instead of foo, and y^(blah) instead of bar. You need to figure out what $i$ is, and also what $i^t=$blah is.– Steve D
Aug 28 at 16:30
@BuddhiniAngelika: Once you pick $i$, you would write
x^i instead of foo, and y^(blah) instead of bar. You need to figure out what $i$ is, and also what $i^t=$blah is.– Steve D
Aug 28 at 16:30
add a comment |Â
1
Your question is ambiguous - you need to give the action of $mathbbZ_3$. For example, it may act trivially on one of the $mathbbZ_7$-factors, but not the other.
– user1729
Aug 28 at 14:35
2
Also, this question is pretty "low-effort" on your part - why can't you just google it? (In fact, I just googled it and found a worked example in the GAP documentation: gap-system.org/Manuals/doc/ref/chap49_mj.html)
– user1729
Aug 28 at 14:37
I tried according to the information in that link, but at the stage I'm trying to enter AutomorphismGroup() command I'm getting an error saying no method found. That's why I asked... Please help now, I have edited the question by including the description of the group.
– Buddhini Angelika
Aug 28 at 16:17
2
I suggest to edit your question to show what exactly you have tried in GAP. We need to see the actual code and the no-method-found message to suggest something. This will also place the question into the reopening queue. Do not post screenshots of GAP, as they are not usable - you need to copy and paste the text from the terminal and indent it by 4 spaces (e.g. like in the answer below).
– Alexander Konovalov
Aug 28 at 20:24
1
If you can describe the action of $Z_3$ through a $2times 2$ matrix over
GF(7), e.g.m:=DiagonalMat([2,4]*One(GF(7)));, you could use the matrix versionSemidirectProduct(Group(m),GF(7)^2);.– ahulpke
Aug 29 at 2:53