List questions from p-groups

Published on 17 Mar 2026 - 10:33

95

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

Published on 17 Mar 2026 - 12:13

64

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The commutator of two subgroup in a finite group

Published on 17 Mar 2026 - 10:55

125

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Group of order 81 acting on a set of order 98

Published on 17 Mar 2026 - 22:58

124

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Group of order $2^{67}$

Published on 17 Mar 2026 - 7:59

554

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$p$-groups in which the centralizers are normal

Published on 17 Mar 2026 - 10:13

322

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Fundamental Theorem of Abelian Groups - intuition regarding Lemma

Published on 17 Mar 2026 - 21:42

79

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

Published on 17 Mar 2026 - 13:11

45

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Determine possible $p$-groups from center and quotient

Published on 17 Mar 2026 - 15:37

80

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Central quotient of $p$-groups

Published on 17 Mar 2026 - 7:11

126

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

Published on 20 Mar 2026 - 9:11

172

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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 25 Mar 2026 - 4:44

969

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

Published on 25 Mar 2026 - 1:17

55

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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 25 Mar 2026 - 4:42

294

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

Published on 20 Mar 2026 - 11:35

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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