# Tagged Questions

Use with the (group-theory) tag. The tag "finite-groups" refers to questions asked in the field of Group Theory which, in particular, focus on the groups of finite order.

1answer
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### Non-isomorphic groups

How to prove that $Z/2\times Z/2$ and $Z/4$ are not isomorphic? I think that $Z/2\times Z/2$ is not cyclic. Hence $Z/2\times Z/2$ and $Z/4$ are not isomorphic. Thank you.
0answers
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### Restricting a representation to a subgroup

This little factoid from algebra quals stumped me: Let $G$ be a finite group and $H \triangleleft G$ an index $2$ subgroup. If we take an irreducible complex representation $V$ of $G$ and restrict it ...
0answers
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### Product of the elements cannot be 1

I have to show in a group $G$ of order $4k+2$ the product of the elements cannot be $1$. What I got so far is that there exists a subgroup $H$ of index $2$ in $G$ (considering left regular ...
2answers
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### Group theory and group representation

I am fairly new to group theory and representation. I am currently looking at faithful representations. I am not quite sure what is the "use" of a faithful representation. I cannot find any "easy to ...
0answers
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### Abelian group action exercise

Let $X$ be a set with $n$ elements and let $G$ be an abelian group acting on $X$ such that: $$(i) \space gx=x \space \forall x \implies g=1,$$ $$(ii) \space \forall x,y \in X, \exists g: gx=y.$$ Show ...
1answer
167 views

### There are no simple groups of order $27p$

Statement Show that there are no simple groups of order $27p$ for any $p$ prime number. I got stuck with this problem, I'll write what I've done so far: Suppose $G$ is a group with $|G|=3^3p$, $p$ ...
2answers
344 views

2answers
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