List questions from maximal-subgroup

Published on 22 Mar 2026 - 15:30

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Generating Prüfer 2-group without its Frattini Subgroup

Published on 22 Mar 2026 - 15:31

223

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$G$ is a group of order $pq$ and $P_q$ and $P_p$ are Sylow subgroups...

Published on 22 Mar 2026 - 18:25

1.3k

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$(\mathbb{Q},+)$ has no maximal subgroup.

Published on 23 Mar 2026 - 9:46

208

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Example of a group where a proper subgroup is not included in a maximal element

Published on 22 Mar 2026 - 15:49

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Prove $\hat{G}\rtimes Aut(G)$ is primitive when $G$ is characteristically simple

Published on 20 Mar 2026 - 8:25

81

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How can we describe all maximal proper subgroups of $G \times G$

Published on 22 Mar 2026 - 22:32

79

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Why $a,b$ assumed coprime?

Published on 22 Mar 2026 - 12:15

70

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Why does ergodicity fail?

Published on 23 Mar 2026 - 9:42

353

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Intersection of all maximal subgroups of a finite group

Published on 23 Mar 2026 - 12:13

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Let $G$ be transitive on $S$. Show that the action is primitive if and only if every $\operatorname{Stab}_G(a), a\in S$, is a maximal subgroup of $G$.

Published on 23 Mar 2026 - 1:33

214

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Let $G$ be a non-abelian finite $p$-group, do we have $Z(G) \leq \Phi(G)$ in general?

Published on 17 Mar 2026 - 5:27

977

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Understanding proof that exponential map of compact connected Lie group is surjective

Published on 17 Mar 2026 - 6:05

136

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Minimal order of a counterexample to Wall’s conjecture

Published on 17 Mar 2026 - 13:50

51

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Quotient by maximal normal locally finite subgroup

Published on 17 Mar 2026 - 16:41

List Question

Number of nonidentity Elements Contained in Conjugates of $M$

Generating Prüfer 2-group without its Frattini Subgroup

$G$ is a group of order $pq$ and $P_q$ and $P_p$ are Sylow subgroups...

$(\mathbb{Q},+)$ has no maximal subgroup.

Example of a group where a proper subgroup is not included in a maximal element

Prove $\hat{G}\rtimes Aut(G)$ is primitive when $G$ is characteristically simple

How can we describe all maximal proper subgroups of $G \times G$

Why $a,b$ assumed coprime?

Why does ergodicity fail?

Intersection of all maximal subgroups of a finite group

Let $G$ be transitive on $S$. Show that the action is primitive if and only if every $\operatorname{Stab}_G(a), a\in S$, is a maximal subgroup of $G$.

Let $G$ be a non-abelian finite $p$-group, do we have $Z(G) \leq \Phi(G)$ in general?

Understanding proof that exponential map of compact connected Lie group is surjective

Minimal order of a counterexample to Wall’s conjecture

Quotient by maximal normal locally finite subgroup

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