Question

Presentation $\langle x,y\mid x^3=y^3=(xy)^3=1\rangle $ with normal abelian subgroup.

score 147 · Answer 1 · 2026-03-26 03:12:46

147

Views

Presentation $\langle x,y\mid x^3=y^3=(xy)^3=1\rangle $ with normal abelian subgroup.

Published on 26 Mar 2026 - 3:12

score 78 · Answer 2 · 2020-01-07 02:37:23

78

Views

Quotient of pure subgroups

Published on 07 Jan 2020 - 2:37

score 166 · Answer 3 · 2020-01-07 08:20:58

166

Views

Group of Endomorphisms

Published on 07 Jan 2020 - 8:20

score 130 · Answer 4 · 2026-03-29 21:54:00

130

Views

Showing a subgroup of $\mathbb{Z}\times\mathbb{Z}$ is cyclic.

Published on 29 Mar 2026 - 21:54

score 448 · Answer 5 · 2020-01-14 10:28:27

448

Views

Showing $\Bbb Z_4 $ and $\Bbb Z_2 \times\Bbb Z_2$ are the only abelian group with $4$ elements.

Published on 14 Jan 2020 - 10:28

score 748 · Answer 6 · 2020-01-14 18:22:32

748

Views

A $\Bbb Z$-module that is not a direct sum of cyclic modules

Published on 14 Jan 2020 - 18:22

score 458 · Answer 7 · 2026-03-25 20:23:30

458

Views

On free abelian groups

Published on 25 Mar 2026 - 20:23

score 164 · Answer 8 · 2026-03-25 20:20:29

164

Views

$G$ abelian $\{ a^ib^j : a^m = b^n = 1, a^2=b^3 \}$, prove that $G=\langle c:c^k=1 \rangle$

Published on 25 Mar 2026 - 20:20

score 431 · Answer 9 · 2020-01-18 17:27:13

431

Views

Abelian Group of order $2^l$ has only one element of order $2$, then this group is cyclic.

Published on 18 Jan 2020 - 17:27

score 1.6k · Answer 10 · 2020-01-18 19:54:58

1.6k

Views

Let $(G,\cdot)$ be a group of order $2n$ with $n$ elements of order $2$. Prove $n$ is odd and $G$ has an abelian subgroup of order $n$.

Published on 18 Jan 2020 - 19:54

score 85 · Answer 11 · 2020-01-20 11:11:55

85

Views

Decomposition of finite abelian groups in primecomponents

Published on 20 Jan 2020 - 11:11

score 111 · Answer 12 · 2026-03-26 02:54:36

111

Views

Large abelian subgroups of perfect groups

Published on 26 Mar 2026 - 2:54

score 368 · Answer 13 · 2026-03-26 01:15:55

368

Views

Prove that every abelian cancellation semigroup can be imbedded in a group

Published on 26 Mar 2026 - 1:15

score 1.5k · Answer 14 · 2026-03-28 02:45:01

1.5k

Views

An abelian group $G$ and onto group homomorphism $h: G \longrightarrow \mathbb{Z}$

Published on 28 Mar 2026 - 2:45

score 171 · Answer 15 · 2026-02-23 08:27:47

171

Views

Existence of homomorphism between middle terms of two exact sequences of abelian groups

Published on 23 Feb 2026 - 8:27

List Question

Presentation $\langle x,y\mid x^3=y^3=(xy)^3=1\rangle $ with normal abelian subgroup.

Quotient of pure subgroups

Group of Endomorphisms

Showing a subgroup of $\mathbb{Z}\times\mathbb{Z}$ is cyclic.

Showing $\Bbb Z_4 $ and $\Bbb Z_2 \times\Bbb Z_2$ are the only abelian group with $4$ elements.

A $\Bbb Z$-module that is not a direct sum of cyclic modules

On free abelian groups

$G$ abelian $\{ a^ib^j : a^m = b^n = 1, a^2=b^3 \}$, prove that $G=\langle c:c^k=1 \rangle$

Abelian Group of order $2^l$ has only one element of order $2$, then this group is cyclic.

Let $(G,\cdot)$ be a group of order $2n$ with $n$ elements of order $2$. Prove $n$ is odd and $G$ has an abelian subgroup of order $n$.

Decomposition of finite abelian groups in primecomponents

Large abelian subgroups of perfect groups

Prove that every abelian cancellation semigroup can be imbedded in a group

An abelian group $G$ and onto group homomorphism $h: G \longrightarrow \mathbb{Z}$

Existence of homomorphism between middle terms of two exact sequences of abelian groups

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