Group decomposition and subgroups
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Assume I have a group decomposition in left cosets
$$G = bigsqcup_i a_i H$$
I would like to deduce from that a decomposition of the group intersected with another subgroup N. Is there a way to determine a subset of the $a_i$ such that
$$Gcap N= bigsqcup_i a_i (Hcap N)$$
group-theory
add a comment |Â
up vote
0
down vote
favorite
Assume I have a group decomposition in left cosets
$$G = bigsqcup_i a_i H$$
I would like to deduce from that a decomposition of the group intersected with another subgroup N. Is there a way to determine a subset of the $a_i$ such that
$$Gcap N= bigsqcup_i a_i (Hcap N)$$
group-theory
2
It can't be done. Take, for example, $G=S_3$, $a_1=e, a_2=(123),a_3=(132)$, $H=e,(12)$, $N=e,(13)$.
â ancientmathematician
Sep 4 at 11:42
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Assume I have a group decomposition in left cosets
$$G = bigsqcup_i a_i H$$
I would like to deduce from that a decomposition of the group intersected with another subgroup N. Is there a way to determine a subset of the $a_i$ such that
$$Gcap N= bigsqcup_i a_i (Hcap N)$$
group-theory
Assume I have a group decomposition in left cosets
$$G = bigsqcup_i a_i H$$
I would like to deduce from that a decomposition of the group intersected with another subgroup N. Is there a way to determine a subset of the $a_i$ such that
$$Gcap N= bigsqcup_i a_i (Hcap N)$$
group-theory
group-theory
asked Sep 4 at 11:06
TheStudent
836
836
2
It can't be done. Take, for example, $G=S_3$, $a_1=e, a_2=(123),a_3=(132)$, $H=e,(12)$, $N=e,(13)$.
â ancientmathematician
Sep 4 at 11:42
add a comment |Â
2
It can't be done. Take, for example, $G=S_3$, $a_1=e, a_2=(123),a_3=(132)$, $H=e,(12)$, $N=e,(13)$.
â ancientmathematician
Sep 4 at 11:42
2
2
It can't be done. Take, for example, $G=S_3$, $a_1=e, a_2=(123),a_3=(132)$, $H=e,(12)$, $N=e,(13)$.
â ancientmathematician
Sep 4 at 11:42
It can't be done. Take, for example, $G=S_3$, $a_1=e, a_2=(123),a_3=(132)$, $H=e,(12)$, $N=e,(13)$.
â ancientmathematician
Sep 4 at 11:42
add a comment |Â
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It can't be done. Take, for example, $G=S_3$, $a_1=e, a_2=(123),a_3=(132)$, $H=e,(12)$, $N=e,(13)$.
â ancientmathematician
Sep 4 at 11:42