List questions from finite-groups

Published on 05 May 2026 - 9:46

82

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For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$

Published on 04 May 2026 - 15:13

46

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Assuming unitarity of arbitrary representations in proof of Schur's lemma

Published on 05 May 2026 - 17:29

72

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existence of subgroups of finite abelian groups

Published on 05 May 2026 - 5:00

138

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Online reference about semi-direct products in finite group theory?

Published on 05 May 2026 - 5:54

945

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classify groups of order $p^2$ simple or not

Published on 05 May 2026 - 2:25

477

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Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.

Published on 05 May 2026 - 8:19

441

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The number of conjugacy classes of a finite group

Published on 07 May 2026 - 12:41

195

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Properties of symmetric and alternating characters

Published on 05 May 2026 - 14:38

139

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Finite group, How can I construct solution step-by-step.

Published on 05 May 2026 - 2:31

114

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How to prove that $\frac{1-z}{|1-z|}$ is a root of unity with $z=e^{i\frac{2\pi}{n}}$

Published on 07 May 2026 - 7:35

328

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The condition between $\chi(1)$ and $[G:H]$ which gives us a normal subgroup.

Published on 05 May 2026 - 18:28

72

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How to arrange $p-1$ non-zero elements into $A$ groups of $B$ where $p$ is a prime number

Published on 10 May 2026 - 8:26

61

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$e^{n/e}$ estimate of the maximum order of permutation group element: proof

Published on 03 May 2026 - 17:36

65

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How to embed $F_q^\times $ in $S_n$?

Published on 03 May 2026 - 8:56

List Question

List Conjugacy Classes in GAP?

For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$

Assuming unitarity of arbitrary representations in proof of Schur's lemma

existence of subgroups of finite abelian groups

Online reference about semi-direct products in finite group theory?

classify groups of order $p^2$ simple or not

Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.

The number of conjugacy classes of a finite group

Properties of symmetric and alternating characters

Finite group, How can I construct solution step-by-step.

How to prove that $\frac{1-z}{|1-z|}$ is a root of unity with $z=e^{i\frac{2\pi}{n}}$

The condition between $\chi(1)$ and $[G:H]$ which gives us a normal subgroup.

How to arrange $p-1$ non-zero elements into $A$ groups of $B$ where $p$ is a prime number

$e^{n/e}$ estimate of the maximum order of permutation group element: proof

How to embed $F_q^\times $ in $S_n$?

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