Question

Show that the group $G$ is Abelian if and only if every irreducible character of $G$ is linear.

score 769 · Answer 1 · 2026-04-16 00:10:44

769

Views

Show that the group $G$ is Abelian if and only if every irreducible character of $G$ is linear.

Published on 16 Apr 2026 - 0:10

score 781 · Answer 2 · 2026-04-14 09:18:13

781

Views

The group $G$ is Abelian iff every irreducible character is linear.

Published on 14 Apr 2026 - 9:18

score 829 · Answer 3 · 2026-05-02 23:51:39

829

Views

Example for subgroups $H$ and $K$ where $HK = K H$ and neither $H$ nor $K$ is normal?

Published on 02 May 2026 - 23:51

score 59 · Answer 4 · 2026-04-29 12:46:25

59

Views

Terminology: reversing the order of the generators.

Published on 29 Apr 2026 - 12:46

score 411 · Answer 5 · 2026-04-29 12:41:14

411

Views

Problem on internal and external direct product?

Published on 29 Apr 2026 - 12:41

score 650 · Answer 6 · 2026-04-18 19:04:21

650

Views

Show that the group $\mathbb Z_{45}$ has exactly one subgroup of order $3$ and construct it.

Published on 18 Apr 2026 - 19:04

score 490 · Answer 7 · 2026-04-25 21:54:35

490

Views

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

Published on 25 Apr 2026 - 21:54

score 376 · Answer 8 · 2026-05-07 12:46:45

376

Views

Showing that $2$ of the following groups are not isomorphic

Published on 07 May 2026 - 12:46

score 411 · Answer 9 · 2026-04-13 18:25:53

411

Views

Center $Z(G)$ of a group $G$ and applications within an exam problem

Published on 13 Apr 2026 - 18:25

score 202 · Answer 10 · 2026-04-25 21:54:35

202

Views

Torsion subgroup combined with normal subgroup!

Published on 25 Apr 2026 - 21:54

score 681 · Answer 11 · 2026-05-03 09:03:09

681

Views

Exams exercise involving the permutation group $S_5$

Published on 03 May 2026 - 9:03

score 489 · Answer 12 · 2026-04-25 21:57:46

489

Views

Two abelian groups are isomorphic iff their corresponding sylow subgroups are isomorphic.

Published on 25 Apr 2026 - 21:57

score 3.3k · Answer 13 · 2026-05-05 16:22:35

3.3k

Views

A finite automaton that accepts at least three $a$s and at least two $b$s.

Published on 05 May 2026 - 16:22

score 2.4k · Answer 14 · 2026-05-04 04:04:30

2.4k

Views

A Gift Problem for the Year 2018

Published on 04 May 2026 - 4:04

score 31 · Answer 15 · 2026-04-16 13:25:24

31

Views

$g^x = g^{x\bmod m}$ in a finite group of order $m$

Published on 16 Apr 2026 - 13:25

List Question

Show that the group $G$ is Abelian if and only if every irreducible character of $G$ is linear.

The group $G$ is Abelian iff every irreducible character is linear.

Example for subgroups $H$ and $K$ where $HK = K H$ and neither $H$ nor $K$ is normal?

Terminology: reversing the order of the generators.

Problem on internal and external direct product?

Show that the group $\mathbb Z_{45}$ has exactly one subgroup of order $3$ and construct it.

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

Showing that $2$ of the following groups are not isomorphic

Center $Z(G)$ of a group $G$ and applications within an exam problem

Torsion subgroup combined with normal subgroup!

Exams exercise involving the permutation group $S_5$

Two abelian groups are isomorphic iff their corresponding sylow subgroups are isomorphic.

A finite automaton that accepts at least three $a$s and at least two $b$s.

A Gift Problem for the Year 2018

$g^x = g^{x\bmod m}$ in a finite group of order $m$

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