List questions from infinite-groups

Published on 25 Mar 2026 - 19:17

67

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Is a sufficient condition that $H$, $K$ $\leq G$ such that $|H|=|K|$ and $[G:H]$ are finites to conclude that $[G:K]=[G:H]$?

Published on 05 Jul 2023 - 21:13

464

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Does this group with prime order elements exist?

Published on 07 Jul 2023 - 14:12

67

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Finitely generated group with a unique maximal subgroup. Is it cyclic?

Published on 10 Jul 2023 - 14:03

71

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Proving object cannot be profinite without Stone topology

Published on 25 Mar 2026 - 20:52

32

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$\prod_p \mathbb{Z}/p\mathbb{Z}$ is not the direct sum of $\bigoplus_p \mathbb{Z}/p\mathbb{Z}$ and a torsion-free subgroup

Published on 26 Mar 2026 - 12:50

60

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Is every subgroup of a profinite group contained in a maximal subgroup?

Published on 25 Mar 2026 - 20:52

146

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Is every closed subgroup of a profinite group contained in a maximal subgroup?

Published on 25 Mar 2026 - 20:52

552

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Subgroups of the $p$-adics that miss $\mathbb{Z}$

Published on 25 Mar 2026 - 20:52

119

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Continuous action by profinite completion of a group

Published on 25 Mar 2026 - 20:52

27

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Upper Bound On the Average Of $(\phi_n-n)$ For $\phi\in S_\infty$

Published on 26 Jul 2023 - 22:50

78

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Decomposition of infinite abelian groups

Published on 26 Mar 2026 - 12:45

25

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Does $B(BE\dot{\cup} E)\subset BE\dot{\cup} E$ imply that $B$ is a sub-semigroup?

Published on 25 Mar 2026 - 3:07

138

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Show that $S$ has Lebesgue measure zero.

Published on 25 Mar 2026 - 12:49

101

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Notation $\pi(G)$ for a group $G$

Published on 19 Aug 2023 - 13:07

List Question

Do profinite groups admit maximal subgroups

Is a sufficient condition that $H$, $K$ $\leq G$ such that $|H|=|K|$ and $[G:H]$ are finites to conclude that $[G:K]=[G:H]$?

Does this group with prime order elements exist?

Finitely generated group with a unique maximal subgroup. Is it cyclic?

Proving object cannot be profinite without Stone topology

$\prod_p \mathbb{Z}/p\mathbb{Z}$ is not the direct sum of $\bigoplus_p \mathbb{Z}/p\mathbb{Z}$ and a torsion-free subgroup

Is every subgroup of a profinite group contained in a maximal subgroup?

Is every closed subgroup of a profinite group contained in a maximal subgroup?

Subgroups of the $p$-adics that miss $\mathbb{Z}$

Continuous action by profinite completion of a group

Upper Bound On the Average Of $(\phi_n-n)$ For $\phi\in S_\infty$

Decomposition of infinite abelian groups

Does $B(BE\dot{\cup} E)\subset BE\dot{\cup} E$ imply that $B$ is a sub-semigroup?

Show that $S$ has Lebesgue measure zero.

Notation $\pi(G)$ for a group $G$

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