List questions from maximal-subgroup

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

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

Published on 07 May 2026 - 14:18

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

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

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

Published on 07 May 2026 - 1:44

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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 $G$.

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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 22 Apr 2026 - 17:16

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

Published on 23 Apr 2026 - 6:44

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Minimal order of a counterexample to Wall’s conjecture

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Quotient by maximal normal locally finite subgroup

Published on 24 Apr 2026 - 8:30

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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