List questions from finite-groups

Published on 28 Mar 2026 - 6:48

248

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A property of the subgroups lattices

Published on 26 Mar 2026 - 16:04

186

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Finitely generated abelian groups isomorphism

Published on 29 Mar 2026 - 20:12

58

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Does the number of elements of order $r$ equal $\sum_{|x| = r} |x^G|$?

Published on 01 Jan 2015 - 16:28

131

Views

Is there a transitive permutation group satisfying these properties?

Published on 26 Mar 2026 - 16:06

96

Views

Group isomorphic to $\Bbb Z/3\Bbb Z\times \Bbb Z/3\Bbb Z$

Published on 01 Jan 2015 - 19:03

36

Views

Is comaximal equivalent to simple?

Published on 01 Jan 2015 - 20:48

81

Views

What is the most mundane & intuitive meaning of the radical of a finite group?

Published on 01 Jan 2015 - 21:46

1.3k

Views

The finite groups with an irreducible faithful complex representation

Published on 01 Jan 2015 - 22:43

908

Views

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

Published on 23 Feb 2026 - 4:02

2k

Views

A group of order $pqr$ (primes $p > q > r$) has a subgroup of order $qr$

Published on 02 Jan 2015 - 6:05

36

Views

Which inclusions of finite groups are relatively linearly primitive?

Published on 02 Jan 2015 - 12:04

270

Views

Subgroups of Semidirect Product of the elementary abelian group of order 8 by $S_3$

Published on 25 Mar 2026 - 17:21

281

Views

Are the primitive groups linearly primitive?

Published on 26 Mar 2026 - 17:28

33

Views

How we can conclude that $p\nmid \sum_{x\in H}|x^G|$ in a group with some elements of order $2p$?

Published on 02 Jan 2015 - 19:11

List Question

stabilizers and orbits of elements in $S_4$

A property of the subgroups lattices

Finitely generated abelian groups isomorphism

Does the number of elements of order $r$ equal $\sum_{|x| = r} |x^G|$?

Is there a transitive permutation group satisfying these properties?

Group isomorphic to $\Bbb Z/3\Bbb Z\times \Bbb Z/3\Bbb Z$

Is comaximal equivalent to simple?

What is the most mundane & intuitive meaning of the radical of a finite group?

The finite groups with an irreducible faithful complex representation

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

A group of order $pqr$ (primes $p > q > r$) has a subgroup of order $qr$

Which inclusions of finite groups are relatively linearly primitive?

Subgroups of Semidirect Product of the elementary abelian group of order 8 by $S_3$

Are the primitive groups linearly primitive?

How we can conclude that $p\nmid \sum_{x\in H}|x^G|$ in a group with some elements of order $2p$?

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