Question

If $\phi$ and $\psi$ are homomorphisms between groups $G$ and $H$ with $\phi \psi = Id_{H}$, then $G \approx H \oplus \ker \psi$

score 569 · Answer 1 · 2026-03-26 01:18:02

569

Views

If $\phi$ and $\psi$ are homomorphisms between groups $G$ and $H$ with $\phi \psi = Id_{H}$, then $G \approx H \oplus \ker \psi$

Published on 26 Mar 2026 - 1:18

score 86 · Answer 2 · 2026-03-25 23:07:00

86

Views

Continuity of absolute value in topological ordered abelian groups

Published on 25 Mar 2026 - 23:07

score 146 · Answer 3 · 2026-03-25 11:20:08

146

Views

Is the value group of an algebraically closed valued field divisible?

Published on 25 Mar 2026 - 11:20

score 194 · Answer 4 · 2026-03-26 01:23:41

194

Views

Number of homomorphism from $Q_8/\Bbb{Z}(Q_8)$ to $D_4/\Bbb{Z}(D_4).$

Published on 26 Mar 2026 - 1:23

score 61 · Answer 5 · 2018-10-21 12:19:27

61

Views

Determine whether $G= \{ a+b\sqrt{p} \ \rvert \ a,b \in \mathbb{Q}, \ a^2+b^2 \neq 0, \ p \text{ is a fixed prime number} \} $ is a group

Published on 21 Oct 2018 - 12:19

score 79 · Answer 6 · 2018-10-22 01:28:45

79

Views

What is the structure of the multiplicative group of the ring $\mathbb{Z}_{p^k } $?

Published on 22 Oct 2018 - 1:28

score 452 · Answer 7 · 2018-10-22 04:22:03

452

Views

Decomposing an abelian group as the image and kernel of a retraction (Rotman 0.1)

Published on 22 Oct 2018 - 4:22

score 70 · Answer 8 · 2026-03-23 09:42:40

70

Views

Why does ergodicity fail?

Published on 23 Mar 2026 - 9:42

score 85 · Answer 9 · 2026-03-25 06:05:50

85

Views

Subgroups of semi-direct products of two elementary abelian subgroups.

Published on 25 Mar 2026 - 6:05

score 72 · Answer 10 · 2026-03-25 06:06:29

72

Views

Prove that $\exists b\in \Bbb Z$ s.t $x^{ab}=x$.(A semi Direct Product question)

Published on 25 Mar 2026 - 6:06

score 146 · Answer 11 · 2018-10-29 21:38:40

146

Views

If $a^{3}=a$ for all $a\in R$, show that the ring $R$ is commutative.

Published on 29 Oct 2018 - 21:38

score 139 · Answer 12 · 2018-10-31 03:19:56

139

Views

$Hol(\Bbb Z_2 \times \Bbb Z_2)$

Published on 31 Oct 2018 - 3:19

score 938 · Answer 13 · 2018-11-01 16:55:35

938

Views

Number of non-isomorphic abelian groups of a given fixed order

Published on 01 Nov 2018 - 16:55

score 114 · Answer 14 · 2018-11-02 18:33:09

114

Views

Show that a subgroup of order $N \in \mathbb{N}$ is isomorphic to $\mathbb{Z}/n\mathbb{Z} × \mathbb{Z}/nn'\mathbb{Z}$.

Published on 02 Nov 2018 - 18:33

score 103 · Answer 15 · 2018-11-02 22:25:06

103

Views

Theory of ﬁnite Abelian groups on Modular Forms

Published on 02 Nov 2018 - 22:25

List Question

If $\phi$ and $\psi$ are homomorphisms between groups $G$ and $H$ with $\phi \psi = Id_{H}$, then $G \approx H \oplus \ker \psi$

Continuity of absolute value in topological ordered abelian groups

Is the value group of an algebraically closed valued field divisible?

Number of homomorphism from $Q_8/\Bbb{Z}(Q_8)$ to $D_4/\Bbb{Z}(D_4).$

Determine whether $G= \{ a+b\sqrt{p} \ \rvert \ a,b \in \mathbb{Q}, \ a^2+b^2 \neq 0, \ p \text{ is a fixed prime number} \} $ is a group

What is the structure of the multiplicative group of the ring $\mathbb{Z}_{p^k } $?

Decomposing an abelian group as the image and kernel of a retraction (Rotman 0.1)

Why does ergodicity fail?

Subgroups of semi-direct products of two elementary abelian subgroups.

Prove that $\exists b\in \Bbb Z$ s.t $x^{ab}=x$.(A semi Direct Product question)

If $a^{3}=a$ for all $a\in R$, show that the ring $R$ is commutative.

$Hol(\Bbb Z_2 \times \Bbb Z_2)$

Number of non-isomorphic abelian groups of a given fixed order

Show that a subgroup of order $N \in \mathbb{N}$ is isomorphic to $\mathbb{Z}/n\mathbb{Z} × \mathbb{Z}/nn'\mathbb{Z}$.

Theory of ﬁnite Abelian groups on Modular Forms

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