Question

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

score 81 · Answer 1 · 2026-02-23 02:13:49

81

Views

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

Published on 23 Feb 2026 - 2:13

score 43 · Answer 2 · 2023-06-14 20:49:00

43

Views

Explicit construction of an outer isomorphism in a $p$-group.

Published on 14 Jun 2023 - 20:49

score 83 · Answer 3 · 2023-06-19 05:27:06

83

Views

In a nonabelian group of order $p^4$, a maximal normal and abelian subgroup of $G$ is of order $p^3$.

Published on 19 Jun 2023 - 5:27

score 99 · Answer 4 · 2023-07-02 21:05:29

99

Views

Normalizer of subgroup of a finite $p$-group.

Published on 02 Jul 2023 - 21:05

score 49 · Answer 5 · 2023-07-05 05:37:04

49

Views

Proving G in a p-group using the centralizer of its elements

Published on 05 Jul 2023 - 5:37

score 62 · Answer 6 · 2023-07-06 16:26:21

62

Views

Cauchy's theorem for groups use unclear

Published on 06 Jul 2023 - 16:26

score 23 · Answer 7 · 2023-08-04 20:41:15

23

Views

2-groups with abelianization of type (2,2)

Published on 04 Aug 2023 - 20:41

score 81 · Answer 8 · 2026-02-23 02:12:20

81

Views

Prove/disprove: Let $G$ s.t $|G| = p^3 \implies |G'| \leq p$.

Published on 23 Feb 2026 - 2:12

score 114 · Answer 9 · 2023-08-23 06:48:35

114

Views

Conjugacy classes of a non-abelian group of order $p^3$

Published on 23 Aug 2023 - 6:48

score 57 · Answer 10 · 2023-08-24 15:38:01

57

Views

Center of a nonabelian p group can be found by taking the intersections of centers of two suitable maximal subgroups

Published on 24 Aug 2023 - 15:38

score 117 · Answer 11 · 2023-08-24 23:42:06

117

Views

Quotient of a minimal non abelian $p$-group by its center

Published on 24 Aug 2023 - 23:42

score 73 · Answer 12 · 2023-10-03 07:05:35

73

Views

The Number of conjugate classes of a non-abelian group of order $729$

Published on 03 Oct 2023 - 7:05

score 175 · Answer 13 · 2023-10-12 03:15:30

175

Views

The number of double coset of p-group $G$

Published on 12 Oct 2023 - 3:15

score 73 · Answer 14 · 2023-10-12 06:53:33

73

Views

Proof of the Index Property for a Proper Subgroup in Finite $p$-Groups

Published on 12 Oct 2023 - 6:53

score 113 · Answer 15 · 2023-11-01 16:26:30

113

Views

If $H$ is a maximum subgroup of a finite group $G$ of index $p$ then $G$ is cyclic of order $p^n$

Published on 01 Nov 2023 - 16:26

List Question

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

Explicit construction of an outer isomorphism in a $p$-group.

In a nonabelian group of order $p^4$, a maximal normal and abelian subgroup of $G$ is of order $p^3$.

Normalizer of subgroup of a finite $p$-group.

Proving G in a p-group using the centralizer of its elements

Cauchy's theorem for groups use unclear

2-groups with abelianization of type (2,2)

Prove/disprove: Let $G$ s.t $|G| = p^3 \implies |G'| \leq p$.

Conjugacy classes of a non-abelian group of order $p^3$

Center of a nonabelian p group can be found by taking the intersections of centers of two suitable maximal subgroups

Quotient of a minimal non abelian $p$-group by its center

The Number of conjugate classes of a non-abelian group of order $729$

The number of double coset of p-group $G$

Proof of the Index Property for a Proper Subgroup in Finite $p$-Groups

If $H$ is a maximum subgroup of a finite group $G$ of index $p$ then $G$ is cyclic of order $p^n$

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