# 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.

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### What dihedral subgroups occur in the affine general linear group $AGL(2,3)$

I am interested in the subgroup structure of the affine general linear group $AGL(2,3)$, in particular I want to know if they could have dihedral subgroups other then $D_3$ and $D_4$, i.e. the ones of ...
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### If every Sylow's subgroup is cyclic then $G$ is supersolvable.

I've this exercise to resolve : prove that if $G$ is a finite group and all its Sylow subgroups are cyclic then G is supersoluble. My solution follows: is it correct? Thanks to everyone for the help! ...
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### Show that over finite fields of characteristic two the finite group $C_3$ has no nontrivial representation

Let $G = \mathbb Z / 3\mathbb Z$ be the cyclic group of order three. I conjecture that every irreducible representation over a finite field of characteristic $2$ must be trivial. But how to prove this?...
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### On nonabelian $2$-groups of exponent $4$ and center $C_2$.

I am new to this forum, and would like to know whether it is possible to fully classify all nonabelian $2$-groups whose exponent is $4$ and center is $C_2$? Thanks.
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### Let $p$ be a Mersenne prime and $G$ an extension of $C_p$, then we have a subgroup in which $C_p$ has a complement

Let $p$ be an Mersenne prime, i.e. $p + 1$ is a power of $2$. Suppose $G$ is an extension of the cyclic group $C_p$ of order $p$ by a group $\overline H$ isomorphic to $PSL(2, p+1)$ or the Suzuki ...
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### Help in step of the proof of Burnside's $p^aq^b$ theorem (Doerk-Hawkes book)

I'm reading the proof of the $p^aq^b$ Burnside's theorem from the book Finite soluble groups by Doerk and Hawkes. The fifth step of the proof says 2.5. Let $M$ and $H$ be maximal subgroups of $G$ (...
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### Relations between the Latin squares of order n and the groups of order n.

Given a group $g$ of order $n\in \mathbb{N}$, it is clear that its Cayley table has the Latin square property. That is, every row and column of the Cayley table contains precisely the elements of $g$. ...
Let $G$ be a finite group and let $M(G)=H^2(G,\mathbb{C}^*)$ be its Schur multiplier. For "small" groups I can compute the Schur multiplier by hand in terms of corresponding roots of unity. However, ...