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 151 · Answer 1 · 2018-02-20 15:20:03

151

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 20 Feb 2018 - 15:20

score 1.7k · Answer 2 · 2018-02-21 10:37:21

1.7k

Views

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

Published on 21 Feb 2018 - 10:37

score 545 · Answer 3 · 2018-02-21 14:18:59

545

Views

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

Published on 21 Feb 2018 - 14:18

score 296 · Answer 4 · 2018-02-23 11:22:20

296

Views

Finite groups with only one conjugacy class of maximal subgroups

Published on 23 Feb 2018 - 11:22

score 261 · Answer 5 · 2018-02-23 13:39:42

261

Views

A problem about cyclic groups.

Published on 23 Feb 2018 - 13:39

score 61 · Answer 6 · 2018-02-23 18:17:26

61

Views

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

Published on 23 Feb 2018 - 18:17

score 151 · Answer 7 · 2026-03-20 03:19:20

151

Views

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

Published on 20 Mar 2026 - 3:19

score 1.8k · Answer 8 · 2018-02-24 08:29:53

1.8k

Views

Nilpotent iff every maximal subgroup is normal

Published on 24 Feb 2018 - 8:29

score 195 · Answer 9 · 2018-02-24 13:06:45

195

Views

Order of a subgroup generated by two elements

Published on 24 Feb 2018 - 13:06

score 133 · Answer 10 · 2026-03-25 01:27:11

133

Views

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

Published on 25 Mar 2026 - 1:27

score 1k · Answer 11 · 2026-03-22 17:33:00

1k

Views

Completing the Cayley table given certain information

Published on 22 Mar 2026 - 17:33

score 55 · Answer 12 · 2018-02-26 08:54:29

55

Views

Few doubts in the graph of group

Published on 26 Feb 2018 - 8:54

score 155 · Answer 13 · 2018-02-26 12:39:50

155

Views

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

Published on 26 Feb 2018 - 12:39

score 34 · Answer 14 · 2026-03-24 22:01:51

34

Views

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

Published on 24 Mar 2026 - 22:01

score 64 · Answer 15 · 2018-02-26 17:59:43

64

Views

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

Published on 26 Feb 2018 - 17:59

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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