Question

Prove that if $G$ is a group with $(ab)^{2}=a^{2}b^{2}$ for all $a,b\in G$, then $G$ is abelian.

score 201 · Answer 1 · 2026-04-30 10:23:13

201

Views

Prove that if $G$ is a group with $(ab)^{2}=a^{2}b^{2}$ for all $a,b\in G$, then $G$ is abelian.

Published on 30 Apr 2026 - 10:23

score 74 · Answer 2 · 2026-05-10 11:21:47

74

Views

For a group [Z,+] with unlabelled integers, what's an algorithm to determine the positive and negative subsets?

Published on 10 May 2026 - 11:21

score 256 · Answer 3 · 2026-04-30 10:23:14

256

Views

$f(x) = x^6, g(x) = x^{10}$ endomorphisms $\implies G$ is abelian

Published on 30 Apr 2026 - 10:23

score 78 · Answer 4 · 2026-04-30 10:23:13

78

Views

Infinite abelian group splits over pure subgroup

Published on 30 Apr 2026 - 10:23

score 6.2k · Answer 5 · 2026-05-05 04:14:39

6.2k

Views

What is the definition of a free abelian group generated by the set $X$?

Published on 05 May 2026 - 4:14

score 2k · Answer 6 · 2026-04-30 10:23:13

2k

Views

Define $T:\mathbb{Z}_{12}\longrightarrow\mathbb{Z}_{12}$. Then find the number of inner automorphisms.

Published on 30 Apr 2026 - 10:23

score 54 · Answer 7 · 2026-04-30 10:22:18

54

Views

Extension of map between finite abelian groups

Published on 30 Apr 2026 - 10:22

score 150 · Answer 8 · 2026-04-29 12:25:55

150

Views

Computing homology groups, algebra confusion

Published on 29 Apr 2026 - 12:25

score 370 · Answer 9 · 2026-04-30 10:22:19

370

Views

Decompose Induced Representations of Abelian Groups into Irreducibles

Published on 30 Apr 2026 - 10:22

score 124 · Answer 10 · 2026-04-30 10:23:21

124

Views

A strange problem from I.N. Herstein

Published on 30 Apr 2026 - 10:23

score 74 · Answer 11 · 2026-05-05 04:16:22

74

Views

On a special type of finite abelian groups of prime power order

Published on 05 May 2026 - 4:16

score 120 · Answer 12 · 2026-05-10 12:17:17

120

Views

Group theory, subgroup of index 2

Published on 10 May 2026 - 12:17

score 86 · Answer 13 · 2026-04-30 10:22:18

86

Views

Is a set $A=\left\{ z \in C: \left| z\right| = 2\right\}$ an abelian group?

Published on 30 Apr 2026 - 10:22

score 53 · Answer 14 · 2026-04-30 10:23:14

53

Views

Is a set $w \cdot z = w + z + iwz$ an abelian group?

Published on 30 Apr 2026 - 10:23

score 564 · Answer 15 · 2026-04-29 12:45:58

564

Views

Prove G is a nonabelian group of order 20

Published on 29 Apr 2026 - 12:45

List Question

Prove that if $G$ is a group with $(ab)^{2}=a^{2}b^{2}$ for all $a,b\in G$, then $G$ is abelian.

For a group [Z,+] with unlabelled integers, what's an algorithm to determine the positive and negative subsets?

$f(x) = x^6, g(x) = x^{10}$ endomorphisms $\implies G$ is abelian

Infinite abelian group splits over pure subgroup

What is the definition of a free abelian group generated by the set $X$?

Define $T:\mathbb{Z}_{12}\longrightarrow\mathbb{Z}_{12}$. Then find the number of inner automorphisms.

Extension of map between finite abelian groups

Computing homology groups, algebra confusion

Decompose Induced Representations of Abelian Groups into Irreducibles

A strange problem from I.N. Herstein

On a special type of finite abelian groups of prime power order

Group theory, subgroup of index 2

Is a set $A=\left\{ z \in C: \left| z\right| = 2\right\}$ an abelian group?

Is a set $w \cdot z = w + z + iwz$ an abelian group?

Prove G is a nonabelian group of order 20

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