List questions from finite-groups

Published on 25 Mar 2026 - 15:41

55

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Showing $d(\frac{Z_2(G)}{Z(G)})=d(G)d(Z(G))$ if and only if $d(G)=2$.

Published on 25 Mar 2026 - 4:42

25

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Why is $\left(\mathbb F_l^{\times}\right)^2<\mathbb F_l^{\times}$

Published on 26 Mar 2026 - 11:17

294

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$G = \langle a, b : a^3 = b^2 = (ab)^3 = e \rangle$. Find the order of G.

Published on 25 Mar 2026 - 13:55

106

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Groups whose minimal number of generators is $\log_2(|G|)$

Published on 25 Mar 2026 - 7:42

204

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Is a finite group union of its cyclic subgroups with trival intersection?

Published on 26 Mar 2026 - 2:51

841

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Example of finite non-abelian group with nontrivial intersection of subgroups

Published on 30 May 2018 - 16:58

49

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Show that the Quotient Group $Γ_2(p)/Γ_2(p^k)$ is finite.

Published on 22 Mar 2026 - 13:43

170

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Finite simple group $G$ containing no elements of order $5$

Published on 25 Mar 2026 - 6:02

688

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More understanding of Schur's Lemma (representation theory)

Published on 31 May 2018 - 20:27

52

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Permutation groups of S_3

Published on 01 Jun 2018 - 12:53

216

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Groups for which all normal subgroups are perfect

Published on 24 Mar 2026 - 23:59

205

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Minimal degree representation of finite simple groups

Published on 25 Mar 2026 - 0:01

435

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Monomial characters of direct product

Published on 25 Mar 2026 - 1:22

133

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A problem with lemma about cyclic groups

Published on 26 Mar 2026 - 6:18

List Question

Invertible elements of $\Bbb{F}_p[x]/\langle x^{p+1}\rangle$?

Showing $d(\frac{Z_2(G)}{Z(G)})=d(G)d(Z(G))$ if and only if $d(G)=2$.

Why is $\left(\mathbb F_l^{\times}\right)^2<\mathbb F_l^{\times}$

$G = \langle a, b : a^3 = b^2 = (ab)^3 = e \rangle$. Find the order of G.

Groups whose minimal number of generators is $\log_2(|G|)$

Is a finite group union of its cyclic subgroups with trival intersection?

Example of finite non-abelian group with nontrivial intersection of subgroups

Show that the Quotient Group $Γ_2(p)/Γ_2(p^k)$ is finite.

Finite simple group $G$ containing no elements of order $5$

More understanding of Schur's Lemma (representation theory)

Permutation groups of S_3

Groups for which all normal subgroups are perfect

Minimal degree representation of finite simple groups

Monomial characters of direct product

A problem with lemma about cyclic groups

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