List questions from p-groups

Published on 06 Jan 2022 - 20:05

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Show ${\rm Aut}(G)$ is a $2$-group, where $G$ is given by a particular presentation

Published on 10 Jan 2022 - 20:19

168

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Each extra-special group of order $2^{2n+1}$ is a central product of $D_8$s or of $D_8$s and a single $Q_8$.

Published on 16 Jan 2022 - 16:04

97

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Groups of order $16$ and their subgroups of index $2$

Published on 26 Jan 2022 - 8:39

55

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On $p$ subgroup of automorphisms of infinite abelian $p$ group

Published on 28 Mar 2026 - 6:00

98

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Self-centralizing subgroups of order $p^2$ in $p$-groups of maximal class

Published on 26 Mar 2026 - 7:58

29

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Proportion of 2-generated $p$-groups of a given order

Published on 21 Feb 2022 - 8:17

52

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Relationship between agemo subgroup and Frattini subgroup in $2$-groups

Published on 08 Mar 2022 - 13:02

397

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Character table of modular Heisenberg groups

Published on 23 Feb 2026 - 21:13

33

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What can we say about $a, b \in G$ when $na = nb$ with $G$ a $p$-group and $(n, p) = 1$?

Published on 21 Mar 2022 - 18:19

251

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Suppose $G$ is group of order $p^k$ for $p$ prime and $k$ positive integer. Prove $G$ must contain an element with an order of $p$

Published on 24 Mar 2022 - 1:51

39

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Extending a Property of a p-group by Direct Product

Published on 31 Mar 2022 - 21:46

85

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$G$ has an abelian subgroup $K$ with $|K|\geq p^3$.

Published on 13 Apr 2022 - 0:49

118

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The irreducible representations of a $p$-group

Published on 17 Apr 2022 - 22:24

64

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An example of a finite $p$-group with cyclic and central Frattini subgroup

Published on 25 Mar 2026 - 7:45

List Question

All $p$-groups have a normal subgroup of each possible order.

Show ${\rm Aut}(G)$ is a $2$-group, where $G$ is given by a particular presentation

Each extra-special group of order $2^{2n+1}$ is a central product of $D_8$s or of $D_8$s and a single $Q_8$.

Groups of order $16$ and their subgroups of index $2$

On $p$ subgroup of automorphisms of infinite abelian $p$ group

Self-centralizing subgroups of order $p^2$ in $p$-groups of maximal class

Proportion of 2-generated $p$-groups of a given order

Relationship between agemo subgroup and Frattini subgroup in $2$-groups

Character table of modular Heisenberg groups

What can we say about $a, b \in G$ when $na = nb$ with $G$ a $p$-group and $(n, p) = 1$?

Suppose $G$ is group of order $p^k$ for $p$ prime and $k$ positive integer. Prove $G$ must contain an element with an order of $p$

Extending a Property of a p-group by Direct Product

$G$ has an abelian subgroup $K$ with $|K|\geq p^3$.

The irreducible representations of a $p$-group

An example of a finite $p$-group with cyclic and central Frattini subgroup

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