Question

How can I justify that $a^{2}=e$ and $b^{3}=e$ for an Abelian group of order 6?

score 44 · Answer 1 · 2017-09-27 15:27:53

44

Views

How can I justify that $a^{2}=e$ and $b^{3}=e$ for an Abelian group of order 6?

Published on 27 Sep 2017 - 15:27

score 33 · Answer 2 · 2017-09-28 05:31:10

33

Views

Product of Transposition Confusion

Published on 28 Sep 2017 - 5:31

score 210 · Answer 3 · 2017-09-28 14:04:24

210

Views

Determine whether each of following is cyclic: $\Bbb Z_7, \Bbb Z_9, \Bbb Z_{10}, \Bbb Z_9^{\times}, \Bbb Z_{20}^{\times}$

Published on 28 Sep 2017 - 14:04

score 11.1k · Answer 4 · 2017-09-28 23:54:40

11.1k

Views

Finding all the subgroups of the quaternions

Published on 28 Sep 2017 - 23:54

score 489 · Answer 5 · 2017-09-29 23:12:35

489

Views

Every non-cyclic group $G$ has at least $2$ non-trivial cyclic subgroups

Published on 29 Sep 2017 - 23:12

score 363 · Answer 6 · 2026-03-27 17:04:33

363

Views

Cyclic Groups of Order 8 and homomorphic images

Published on 27 Mar 2026 - 17:04

score 280 · Answer 7 · 2017-10-03 09:13:55

280

Views

the number of solutions $x$ of the equation $x^m=e$ in $G$ is exactly $m$?

Published on 03 Oct 2017 - 9:13

score 167 · Answer 8 · 2017-10-04 07:05:10

167

Views

Proving that a cyclic group is generated by a single element.

Published on 04 Oct 2017 - 7:05

score 61 · Answer 9 · 2026-04-03 01:33:10

61

Views

Finite Cyclic Group

Published on 03 Apr 2026 - 1:33

score 37 · Answer 10 · 2017-10-06 07:06:16

37

Views

Generators of a group

Published on 06 Oct 2017 - 7:06

score 1.1k · Answer 11 · 2017-10-06 10:04:21

1.1k

Views

Does element of order zero and element of order infinity in a group mean the same?

Published on 06 Oct 2017 - 10:04

score 872 · Answer 12 · 2017-10-07 01:48:44

872

Views

What is the cyclic subgroup of integers(Z) generated by -1 under +?

Published on 07 Oct 2017 - 1:48

score 371 · Answer 13 · 2017-10-07 22:41:40

371

Views

Distinct generators of a finite cyclic group.

Published on 07 Oct 2017 - 22:41

score 5.5k · Answer 14 · 2017-10-08 00:46:47

5.5k

Views

Finding cyclic subgroups of a non-cyclic group

Published on 08 Oct 2017 - 0:46

score 1k · Answer 15 · 2017-10-09 05:36:56

1k

Views

Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$

Published on 09 Oct 2017 - 5:36

List Question

How can I justify that $a^{2}=e$ and $b^{3}=e$ for an Abelian group of order 6?

Product of Transposition Confusion

Determine whether each of following is cyclic: $\Bbb Z_7, \Bbb Z_9, \Bbb Z_{10}, \Bbb Z_9^{\times}, \Bbb Z_{20}^{\times}$

Finding all the subgroups of the quaternions

Every non-cyclic group $G$ has at least $2$ non-trivial cyclic subgroups

Cyclic Groups of Order 8 and homomorphic images

the number of solutions $x$ of the equation $x^m=e$ in $G$ is exactly $m$?

Proving that a cyclic group is generated by a single element.

Finite Cyclic Group

Generators of a group

Does element of order zero and element of order infinity in a group mean the same?

What is the cyclic subgroup of integers(Z) generated by -1 under +?

Distinct generators of a finite cyclic group.

Finding cyclic subgroups of a non-cyclic group

Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$

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