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Shaun
Shaun
8:15 PM
Yes, I think so, @BuddhiniAngelika, but don't quote me on it!
I'm trying to answer the following . . .
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Q: Is the subgroup $H:=\langle xyxy\rangle$ normal in $G:=\langle x,y\mid x^3=e, y^2=e\rangle$? If so, find $G/H$.

David MolanoLet $G=\langle x,y\mid x^3=e, y^2=e\rangle$ and otherwise unrestricted. Let $H=\langle xyxy\rangle$. Is $H\triangleleft G$? And in that case, what is $$G/H$$ isomorphic to? If it is a normal subgroup, I'd suspect $G/H\cong D_3$, but is that really true?

group-theory normal-subgroups group-presentation combinatorial-group-theory
Here's what I have so far . . .
(Please hang on while I find an appropriate way to share it here . . . )
The link above is to an edit of a sandpit answer containing my draft of my thoughts so far. The notation is, in hindsight, overcomplicated, but I was thinking about the problem as I was typing so . . .
Yeah.
 
Shaun
Shaun
8:53 PM
I was looking into this and similar results . . .
 

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