Question

If $xy = yx$ and $\lvert x\rvert$ and $\lvert y\rvert$ are coprime, then $\lvert xy\rvert = lcm(\lvert x\rvert, \lvert y\rvert)$

score 154 · Answer 1 · 2026-04-16 08:31:55

154

Views

If $xy = yx$ and $\lvert x\rvert$ and $\lvert y\rvert$ are coprime, then $\lvert xy\rvert = lcm(\lvert x\rvert, \lvert y\rvert)$

Published on 16 Apr 2026 - 8:31

score 1.7k · Answer 2 · 2026-05-10 12:34:25

1.7k

Views

Proof that (Z3, +) is isomorphic C3, and (Z3, +) is a proper subgroup of S3

Published on 10 May 2026 - 12:34

score 553 · Answer 3 · 2026-05-10 13:26:23

553

Views

How do you show $\mathbb{Z}_{3}$ is a proper normal subgroup of $S_{3}$?

Published on 10 May 2026 - 13:26

score 299 · Answer 4 · 2026-04-14 12:20:20

299

Views

Finite groups with only one conjugacy class of maximal subgroups

Published on 14 Apr 2026 - 12:20

score 264 · Answer 5 · 2026-04-08 23:25:05

264

Views

A problem about cyclic groups.

Published on 08 Apr 2026 - 23:25

score 64 · Answer 6 · 2026-04-11 16:32:33

64

Views

Help in understanding a proof of Milne about the order of a product of elements in a group

Published on 11 Apr 2026 - 16:32

score 159 · Answer 7 · 2026-05-07 12:43:27

159

Views

Does the existence of infinite number of Leinster groups indicate the existence of infinite number of perfect numbers?

Published on 07 May 2026 - 12:43

score 1.8k · Answer 8 · 2026-04-15 01:06:40

1.8k

Views

Nilpotent iff every maximal subgroup is normal

Published on 15 Apr 2026 - 1:06

score 198 · Answer 9 · 2026-04-15 08:15:32

198

Views

Order of a subgroup generated by two elements

Published on 15 Apr 2026 - 8:15

score 141 · Answer 10 · 2026-05-10 12:16:05

141

Views

I believe all groups are necessarily finitely or infinitely generated. Is that correct?

Published on 10 May 2026 - 12:16

score 1k · Answer 11 · 2026-04-20 13:15:36

1k

Views

Completing the Cayley table given certain information

Published on 20 Apr 2026 - 13:15

score 58 · Answer 12 · 2026-04-16 03:25:59

58

Views

Few doubts in the graph of group

Published on 16 Apr 2026 - 3:25

score 158 · Answer 13 · 2026-04-15 11:58:52

158

Views

Lower exponent-p central series ends in {1} for finite p-groups

Published on 15 Apr 2026 - 11:58

score 39 · Answer 14 · 2026-05-10 12:17:17

39

Views

Does a transversal of a Sylow-2 subgroup provide an involution cover?

Published on 10 May 2026 - 12:17

score 67 · Answer 15 · 2026-04-15 05:47:36

67

Views

How many subgroups of $Z_2^n$ are there $\textbf{not}$ up to isomorphism?

Published on 15 Apr 2026 - 5:47

List Question

If $xy = yx$ and $\lvert x\rvert$ and $\lvert y\rvert$ are coprime, then $\lvert xy\rvert = lcm(\lvert x\rvert, \lvert y\rvert)$

Proof that (Z3, +) is isomorphic C3, and (Z3, +) is a proper subgroup of S3

How do you show $\mathbb{Z}_{3}$ is a proper normal subgroup of $S_{3}$?

Finite groups with only one conjugacy class of maximal subgroups

A problem about cyclic groups.

Help in understanding a proof of Milne about the order of a product of elements in a group

Does the existence of infinite number of Leinster groups indicate the existence of infinite number of perfect numbers?

Nilpotent iff every maximal subgroup is normal

Order of a subgroup generated by two elements

I believe all groups are necessarily finitely or infinitely generated. Is that correct?

Completing the Cayley table given certain information

Few doubts in the graph of group

Lower exponent-p central series ends in {1} for finite p-groups

Does a transversal of a Sylow-2 subgroup provide an involution cover?

How many subgroups of $Z_2^n$ are there $\textbf{not}$ up to isomorphism?

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