Question

Maximal Order of Elements in Finite Abelian Group

score 206 · Answer 1 · 2026-03-29 20:06:17

206

Views

Maximal Order of Elements in Finite Abelian Group

Published on 29 Mar 2026 - 20:06

score 62 · Answer 2 · 2019-12-15 05:40:16

62

Views

Number of elements with order $2$

Published on 15 Dec 2019 - 5:40

score 355 · Answer 3 · 2026-03-29 20:05:41

355

Views

A finite abelian group in which each element has order 1 or $p$, $p$ prime, is an elementary abelian group

Published on 29 Mar 2026 - 20:05

score 94 · Answer 4 · 2019-12-18 01:11:54

94

Views

Can an abelian subgroup of $SO(4)$ be diagonalised over $\mathbb{C}$?

Published on 18 Dec 2019 - 1:11

score 862 · Answer 5 · 2019-12-18 18:41:20

862

Views

Let $G$ be a group. Show that if $H$ is subgroup of $G$ then $HG'$ is normal subgroup of $G$.

Published on 18 Dec 2019 - 18:41

score 352 · Answer 6 · 2026-03-28 00:49:30

352

Views

Find all group homomorphisms from $\mathbb{Q}$ to $GL_n(\mathbb{C})$

Published on 28 Mar 2026 - 0:49

score 140 · Answer 7 · 2026-03-29 06:47:37

140

Views

Consider $H=\Bbb{Z}_{30}$ and $G=\Bbb{Z}_{15}$ as additive abelian groups. Show that ${\rm Aut}(H) \cong {\rm Aut}(G)$.

Published on 29 Mar 2026 - 6:47

score 866 · Answer 8 · 2026-03-29 20:04:49

866

Views

Is every Abelian group isomorphic to the external direct product of two cyclic groups?

Published on 29 Mar 2026 - 20:04

score 295 · Answer 9 · 2026-03-27 21:40:03

295

Views

Existence of a commutative inverse semigroup with no identity element

Published on 27 Mar 2026 - 21:40

score 1.7k · Answer 10 · 2026-03-28 00:50:52

1.7k

Views

How to show that $\phi(g)=g^{-1}$ is a group homomorphism iff $G$ is abelian?

Published on 28 Mar 2026 - 0:50

score 61 · Answer 11 · 2026-03-27 21:56:58

61

Views

Find the factor groups of the $\mathbb{Z}/252\mathbb{Z}$ which are projective $\mathbb{Z}/252\mathbb{Z}$-modules

Published on 27 Mar 2026 - 21:56

score 63 · Answer 12 · 2026-03-26 01:11:58

63

Views

The number of triangles in the Cayley graph of a finite abelian group.

Published on 26 Mar 2026 - 1:11

score 187 · Answer 13 · 2026-03-26 21:26:00

187

Views

Find an injective group homomorphism $\varphi: D_4 → Sym_4$ with $D_4$ being the dihedral group

Published on 26 Mar 2026 - 21:26

score 583 · Answer 14 · 2026-03-28 00:54:11

583

Views

Homomorphism to abelian group

Published on 28 Mar 2026 - 0:54

score 240 · Answer 15 · 2026-03-27 18:08:14

240

Views

Simple proof of Sylow's theorems for Abelian groups?

Published on 27 Mar 2026 - 18:08

List Question

Maximal Order of Elements in Finite Abelian Group

Number of elements with order $2$

A finite abelian group in which each element has order 1 or $p$, $p$ prime, is an elementary abelian group

Can an abelian subgroup of $SO(4)$ be diagonalised over $\mathbb{C}$?

Let $G$ be a group. Show that if $H$ is subgroup of $G$ then $HG'$ is normal subgroup of $G$.

Find all group homomorphisms from $\mathbb{Q}$ to $GL_n(\mathbb{C})$

Consider $H=\Bbb{Z}_{30}$ and $G=\Bbb{Z}_{15}$ as additive abelian groups. Show that ${\rm Aut}(H) \cong {\rm Aut}(G)$.

Is every Abelian group isomorphic to the external direct product of two cyclic groups?

Existence of a commutative inverse semigroup with no identity element

How to show that $\phi(g)=g^{-1}$ is a group homomorphism iff $G$ is abelian?

Find the factor groups of the $\mathbb{Z}/252\mathbb{Z}$ which are projective $\mathbb{Z}/252\mathbb{Z}$-modules

The number of triangles in the Cayley graph of a finite abelian group.

Find an injective group homomorphism $\varphi: D_4 → Sym_4$ with $D_4$ being the dihedral group

Homomorphism to abelian group

Simple proof of Sylow's theorems for Abelian groups?

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