List questions from p-groups

Published on 05 May 2026 - 0:30

101

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Some conditions on a finite non-abelian $2$-group

Published on 05 May 2026 - 4:11

74

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The commutator of two subgroup in a finite group

Published on 05 May 2026 - 6:18

131

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Group of order 81 acting on a set of order 98

Published on 29 Apr 2026 - 12:53

131

Views

Group of order $2^{67}$

Published on 10 May 2026 - 9:08

561

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$p$-groups in which the centralizers are normal

Published on 05 May 2026 - 17:57

329

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Fundamental Theorem of Abelian Groups - intuition regarding Lemma

Published on 04 May 2026 - 23:22

86

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Finite $2$-group with derived subgroup of order 8

Published on 05 May 2026 - 6:20

50

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Determine possible $p$-groups from center and quotient

Published on 05 May 2026 - 12:33

85

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Central quotient of $p$-groups

Published on 04 May 2026 - 19:26

133

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Show that the dihedral group $D_{16}$ is the internal direct product of its Sylow subgroups.

Published on 29 Apr 2026 - 12:52

174

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Proof of theorem: If $G$ is a finite nonabelian $p$-group, then $\mathrm{Aut}_c(G)=\mathrm{Inn}(G)$ if and only if $G′=Z(G)$ and $Z(G)$ is cyclic.

Published on 17 Apr 2026 - 19:01

973

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If G is not abelian with order $p^3$ then $G'=Z(G)$

Published on 27 Apr 2026 - 1:27

58

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Showing $d(\frac{Z_2(G)}{Z(G)})=d(G)d(Z(G))$ if and only if $d(G)=2$.

Published on 07 May 2026 - 20:27

299

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Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).

Published on 03 May 2026 - 19:39

List Question

Subgroup of index p in an infinite p-group?

Some conditions on a finite non-abelian $2$-group

The commutator of two subgroup in a finite group

Group of order 81 acting on a set of order 98

Group of order $2^{67}$

$p$-groups in which the centralizers are normal

Fundamental Theorem of Abelian Groups - intuition regarding Lemma

Finite $2$-group with derived subgroup of order 8

Determine possible $p$-groups from center and quotient

Central quotient of $p$-groups

Show that the dihedral group $D_{16}$ is the internal direct product of its Sylow subgroups.

Proof of theorem: If $G$ is a finite nonabelian $p$-group, then $\mathrm{Aut}_c(G)=\mathrm{Inn}(G)$ if and only if $G′=Z(G)$ and $Z(G)$ is cyclic.

If G is not abelian with order $p^3$ then $G'=Z(G)$

Showing $d(\frac{Z_2(G)}{Z(G)})=d(G)d(Z(G))$ if and only if $d(G)=2$.

Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).

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