Intersection of orbits is the orbit of intersection

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Let $G$ be a (topological) group acting on a space $X$. Let $xin X$ and $A,B$ be two subgroups of $G$. Is it true in general that $(Acdot x)cap (Bcdot x)= (Acap B)cdot x$?




group-theory topological-groups




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    Let $G$ be a (topological) group acting on a space $X$. Let $xin X$ and $A,B$ be two subgroups of $G$. Is it true in general that $(Acdot x)cap (Bcdot x)= (Acap B)cdot x$?




    group-theory topological-groups




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      up vote
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      up vote
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      down vote

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      Let $G$ be a (topological) group acting on a space $X$. Let $xin X$ and $A,B$ be two subgroups of $G$. Is it true in general that $(Acdot x)cap (Bcdot x)= (Acap B)cdot x$?




      group-theory topological-groups




      share|cite|improve this question












      Let $G$ be a (topological) group acting on a space $X$. Let $xin X$ and $A,B$ be two subgroups of $G$. Is it true in general that $(Acdot x)cap (Bcdot x)= (Acap B)cdot x$?





      group-theory topological-groups





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      asked Aug 22 at 10:16









      Amrat A

      915




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          Let $G = C_2 times C_2$ and $X = Bbb Z/2Bbb Z$ and $(g^a,g^b) cdot overline n := overlinea + b + n$ and $A = (e,g), (e,e)$ and $B = (g,e), (e,e)$.



          Then, LHS = $X$ and RHS = $overline 0$.






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            1 Answer
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            up vote
            2
            down vote



            accepted










            Let $G = C_2 times C_2$ and $X = Bbb Z/2Bbb Z$ and $(g^a,g^b) cdot overline n := overlinea + b + n$ and $A = (e,g), (e,e)$ and $B = (g,e), (e,e)$.



            Then, LHS = $X$ and RHS = $overline 0$.






            share|cite|improve this answer
























              up vote
              2
              down vote



              accepted










              Let $G = C_2 times C_2$ and $X = Bbb Z/2Bbb Z$ and $(g^a,g^b) cdot overline n := overlinea + b + n$ and $A = (e,g), (e,e)$ and $B = (g,e), (e,e)$.



              Then, LHS = $X$ and RHS = $overline 0$.






              share|cite|improve this answer






















                up vote
                2
                down vote



                accepted







                up vote
                2
                down vote



                accepted






                Let $G = C_2 times C_2$ and $X = Bbb Z/2Bbb Z$ and $(g^a,g^b) cdot overline n := overlinea + b + n$ and $A = (e,g), (e,e)$ and $B = (g,e), (e,e)$.



                Then, LHS = $X$ and RHS = $overline 0$.






                share|cite|improve this answer












                Let $G = C_2 times C_2$ and $X = Bbb Z/2Bbb Z$ and $(g^a,g^b) cdot overline n := overlinea + b + n$ and $A = (e,g), (e,e)$ and $B = (g,e), (e,e)$.



                Then, LHS = $X$ and RHS = $overline 0$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Aug 22 at 10:38









                Kenny Lau

                19k2157




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