Question

Groups of certain order

score 52 · Answer 1 · 2026-04-14 12:30:54

52

Views

Groups of certain order

Published on 14 Apr 2026 - 12:30

score 106 · Answer 2 · 2026-04-16 11:10:59

106

Views

$\forall m,n \geq 2$, $\exists$ non-cyclic group of order $n^{m}$

Published on 16 Apr 2026 - 11:10

score 1k · Answer 3 · 2026-04-13 10:22:17

1k

Views

If $g$ and $h$ are group elements of order $mn$ what is the order of $(gh)^m$

Published on 13 Apr 2026 - 10:22

score 535 · Answer 4 · 2026-04-16 13:35:43

535

Views

Dicyclic group of order 12 automorphism

Published on 16 Apr 2026 - 13:35

score 78 · Answer 5 · 2026-04-11 10:55:48

78

Views

$\gcd(|H_{1}|,|H_{2}|,\cdots,|H_{n}|) > 1$ implies $H_{1} \times H_{2} \times \cdots \times H_{n} = G$ not cyclic

Published on 11 Apr 2026 - 10:55

score 1.3k · Answer 6 · 2026-04-15 18:20:44

1.3k

Views

Let $G$ be a group with 4 elements. Show that it is abelian.

Published on 15 Apr 2026 - 18:20

score 229 · Answer 7 · 2026-04-10 15:40:54

229

Views

Is every element of a finite group a product of elements of prime order?

Published on 10 Apr 2026 - 15:40

score 568 · Answer 8 · 2026-04-10 21:42:54

568

Views

Set of all homomorphisms of G into the group of nonzero complex numbers under multiplication is Abelian

Published on 10 Apr 2026 - 21:42

score 837 · Answer 9 · 2026-04-13 21:44:50

837

Views

G, a finite abelian and cyclic group, isomorphic to set of homomorphisms of G into C\{0}

Published on 13 Apr 2026 - 21:44

score 792 · Answer 10 · 2026-04-13 23:51:06

792

Views

Nilpotent and cyclic quotient group implies abelian

Published on 13 Apr 2026 - 23:51

score 338 · Answer 11 · 2026-04-17 10:03:01

338

Views

For $g_1,g_2$ in finite abelian group with $g_1\neq g_2$, there is $\phi\in\mathrm{Hom}(G,\mathbb C^\times)$ such that $\phi(g_1)\ne\phi(g_2)$

Published on 17 Apr 2026 - 10:03

score 101 · Answer 12 · 2026-04-14 04:19:29

101

Views

A class of subsets of the sums of $\mathbb{Z}_2$

Published on 14 Apr 2026 - 4:19

score 109 · Answer 13 · 2026-04-16 05:46:45

109

Views

For characters of a finite group, is $\langle\chi_1\cdot\chi_2,1\rangle = \langle\chi_1,1\rangle\cdot\chi_2(1)$?

Published on 16 Apr 2026 - 5:46

score 360 · Answer 14 · 2026-04-17 12:30:27

360

Views

Finding elements of a particular order in the direct product of abelian groups

Published on 17 Apr 2026 - 12:30

score 1k · Answer 15 · 2026-04-08 16:41:26

1k

Views

Understanding group structure using GAP

Published on 08 Apr 2026 - 16:41

List Question

Groups of certain order

$\forall m,n \geq 2$, $\exists$ non-cyclic group of order $n^{m}$

If $g$ and $h$ are group elements of order $mn$ what is the order of $(gh)^m$

Dicyclic group of order 12 automorphism

$\gcd(|H_{1}|,|H_{2}|,\cdots,|H_{n}|) > 1$ implies $H_{1} \times H_{2} \times \cdots \times H_{n} = G$ not cyclic

Let $G$ be a group with 4 elements. Show that it is abelian.

Is every element of a finite group a product of elements of prime order?

Set of all homomorphisms of G into the group of nonzero complex numbers under multiplication is Abelian

G, a finite abelian and cyclic group, isomorphic to set of homomorphisms of G into C\{0}

Nilpotent and cyclic quotient group implies abelian

For $g_1,g_2$ in finite abelian group with $g_1\neq g_2$, there is $\phi\in\mathrm{Hom}(G,\mathbb C^\times)$ such that $\phi(g_1)\ne\phi(g_2)$

A class of subsets of the sums of $\mathbb{Z}_2$

For characters of a finite group, is $\langle\chi_1\cdot\chi_2,1\rangle = \langle\chi_1,1\rangle\cdot\chi_2(1)$?

Finding elements of a particular order in the direct product of abelian groups

Understanding group structure using GAP

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