List questions from p-groups

Published on 15 May 2021 - 9:40

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Definitions of solvable group

Published on 28 Mar 2026 - 1:12

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Abelian divisible p-groups and Prüfer group

Published on 23 Feb 2026 - 6:19

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Quaternion group as a central extension of a $2$-group

Published on 21 Mar 2026 - 11:54

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Let $G$ be a $p$-group. If every two maximal subgroups of $G$ are conjugated, then $G$ is cyclic

Published on 25 Mar 2026 - 15:42

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Let $P$ be a $p$-subgroup of a finite group $G$. Prove that $[G:P]$ is congruent to $[N_G(P):P]\bmod p$.

Published on 19 Jun 2021 - 9:13

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A question on normal noncyclic abelian subgroups

Published on 25 Jun 2021 - 12:37

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Showing $|G|=p^r \Rightarrow |G| \equiv |Z(G)| \pmod{p}$

Published on 11 Jul 2021 - 17:44

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Is there a systematic way to find the center of a finitely-presented, finite $p$ group?

Published on 27 Mar 2026 - 17:53

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Without using the class equation, prove that a p-group G (for p prime) has normal subgroups of all orders dividing the order of G.

Published on 03 Aug 2021 - 2:42

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Let $|G|=p^7$ and $K\le G$ with $|K|=p^3$. Then $\exists M\le G$ of order $p^4$ such that $K \trianglelefteq M$.

Published on 14 Aug 2021 - 23:08

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Subgroups of $p$-group containing element of order $p$

Published on 16 Aug 2021 - 2:25

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An abelian $p$-group has finitely many elements of each order iff it satisfies ${\rm min}$

Published on 28 Mar 2026 - 2:08

86

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A question about the names of the non-abelian groups of order $p^3$.

Published on 19 Aug 2021 - 12:08

103

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Center of semi-direct product

Published on 22 Aug 2021 - 18:27

List Question

Show that a group of order $175$ is not simple.

Definitions of solvable group

Abelian divisible p-groups and Prüfer group

Quaternion group as a central extension of a $2$-group

Let $G$ be a $p$-group. If every two maximal subgroups of $G$ are conjugated, then $G$ is cyclic

Let $P$ be a $p$-subgroup of a finite group $G$. Prove that $[G:P]$ is congruent to $[N_G(P):P]\bmod p$.

A question on normal noncyclic abelian subgroups

Showing $|G|=p^r \Rightarrow |G| \equiv |Z(G)| \pmod{p}$

Is there a systematic way to find the center of a finitely-presented, finite $p$ group?

Without using the class equation, prove that a p-group G (for p prime) has normal subgroups of all orders dividing the order of G.

Let $|G|=p^7$ and $K\le G$ with $|K|=p^3$. Then $\exists M\le G$ of order $p^4$ such that $K \trianglelefteq M$.

Subgroups of $p$-group containing element of order $p$

An abelian $p$-group has finitely many elements of each order iff it satisfies ${\rm min}$

A question about the names of the non-abelian groups of order $p^3$.

Center of semi-direct product

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