Question

If $G$ is finite and every subgroup is characteristic then $G$ is abelian and cyclic

score 286 · Answer 1 · 2019-10-18 17:16:01

286

Views

If $G$ is finite and every subgroup is characteristic then $G$ is abelian and cyclic

Published on 18 Oct 2019 - 17:16

score 219 · Answer 2 · 2026-03-25 23:36:10

219

Views

Presentation of ${\rm SL}(2,3)$

Published on 25 Mar 2026 - 23:36

score 196 · Answer 3 · 2026-03-29 15:33:22

196

Views

$G$ cyclic group of order $n$ and $g \in G$ generator; then $g^k$ is a generator iff $(k,n)=1$. Is this a valid argument?

Published on 29 Mar 2026 - 15:33

score 108 · Answer 4 · 2026-03-29 23:47:02

108

Views

Prob. 9 (b), Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Every group of order $4$ is abelian

Published on 29 Mar 2026 - 23:47

score 385 · Answer 5 · 2019-10-21 19:13:45

385

Views

Let $G = (\Bbb Z/18\Bbb Z, +)$ be a cyclic group of order $18$.

Published on 21 Oct 2019 - 19:13

score 111 · Answer 6 · 2026-03-29 23:47:03

111

Views

Prob. 9 (c), Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Every group of order $5$ is abelian

Published on 29 Mar 2026 - 23:47

score 128 · Answer 7 · 2026-03-26 04:34:32

128

Views

Image of irreducible representation of degree 2

Published on 26 Mar 2026 - 4:34

score 74 · Answer 8 · 2019-10-23 00:46:33

74

Views

Group Theory Problem from Old GRE questions

Published on 23 Oct 2019 - 0:46

score 120 · Answer 9 · 2019-10-23 01:06:34

120

Views

A Group of Order 6

Published on 23 Oct 2019 - 1:06

score 46 · Answer 10 · 2026-04-09 06:41:55

46

Views

Intersection of isometric subspaces in a space over a finite field

Published on 09 Apr 2026 - 6:41

score 788 · Answer 11 · 2019-10-23 02:07:52

788

Views

Order of the products of two order-2 elements in a finite group

Published on 23 Oct 2019 - 2:07

score 77 · Answer 12 · 2026-03-25 07:46:10

77

Views

Number of Non-equivalent Generating Triples of Involutions in Finite Simple Groups

Published on 25 Mar 2026 - 7:46

score 551 · Answer 13 · 2019-10-23 12:28:53

551

Views

Let $G = ⟨a⟩$ be a cyclic group of order n. For each integer m, define a map $f_m :G−→G$ by $f_m(x)=x^m$ for every $x∈G$

Published on 23 Oct 2019 - 12:28

score 47 · Answer 14 · 2019-10-25 10:34:00

47

Views

The Schur-Zassenhaus Theorem and properties of an associated matrix

Published on 25 Oct 2019 - 10:34

score 594 · Answer 15 · 2026-03-26 04:31:26

594

Views

Conjugacy classes of a quotient group

Published on 26 Mar 2026 - 4:31

List Question

If $G$ is finite and every subgroup is characteristic then $G$ is abelian and cyclic

Presentation of ${\rm SL}(2,3)$

$G$ cyclic group of order $n$ and $g \in G$ generator; then $g^k$ is a generator iff $(k,n)=1$. Is this a valid argument?

Prob. 9 (b), Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Every group of order $4$ is abelian

Let $G = (\Bbb Z/18\Bbb Z, +)$ be a cyclic group of order $18$.

Prob. 9 (c), Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Every group of order $5$ is abelian

Image of irreducible representation of degree 2

Group Theory Problem from Old GRE questions

A Group of Order 6

Intersection of isometric subspaces in a space over a finite field

Order of the products of two order-2 elements in a finite group

Number of Non-equivalent Generating Triples of Involutions in Finite Simple Groups

Let $G = ⟨a⟩$ be a cyclic group of order n. For each integer m, define a map $f_m :G−→G$ by $f_m(x)=x^m$ for every $x∈G$

The Schur-Zassenhaus Theorem and properties of an associated matrix

Conjugacy classes of a quotient group

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