# Tagged Questions

Questions on group theory which concern finite groups.

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### Restriction of $H^3(M_{24}, U(1))$ to $M_{12} \rtimes \mathbb{Z}_2$

$M_{12}\rtimes \mathbb{Z}_2$ is a maximal subgroup of $M_{24}$, where $M_{24}$ and $M_{12}$ are Mathieu groups . Also, it is known that $H^3(M_{24}, U(1)) \cong \mathbb{Z}_{12}$. I want to find the ...
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### Finite groups of order $n$ having exactly $n$ subgroups

Is it known a characterization of finite groups of order $n$ having exactly $n$ subgroups? A supplementary question: are there abelian groups other than the trivial group and $\mathbb{Z}_2$ with ...
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### Number of squares in a finite group

This was asked at MSE but never answered. Let $G$ be a finite group and denote by $sq(G)$ the number of squares in $G$ i.e. the number of elements in $G$ which possess a square root. For example, if ...
### The number of subgroups of ${\frak S}_n$
Because of my interest in this question, I listed the subgroups of ${\frak S}_n$ for $1\le n\le4$. I found that the number of subgroups are, respectively, $1,2,6,24$. It might be a coincidence, or it ...
I've learned that all non-abelian finite simple groups are $2$-generated, i.e. have a generating set of cardinality $2$. Is there a reference to this statement which does not just point to the ...