Question

Non cyclic group of order 125 which has an element of order 25.

score 424 · Answer 1 · 2017-03-06 09:02:48

424

Views

Non cyclic group of order 125 which has an element of order 25.

Published on 06 Mar 2017 - 9:02

score 395 · Answer 2 · 2017-03-06 23:10:22

395

Views

The zero divisors of $\Bbb Z/5\Bbb Z\times \Bbb Z/18\Bbb Z $.

Published on 06 Mar 2017 - 23:10

score 334 · Answer 3 · 2017-03-26 18:22:13

334

Views

Statement on an abelian group being isomorphic to a direct sum of cyclic groups

Published on 26 Mar 2017 - 18:22

score 323 · Answer 4 · 2026-03-26 12:53:51

323

Views

Possible chief factors of a group of order 336

Published on 26 Mar 2026 - 12:53

score 38 · Answer 5 · 2017-04-03 20:58:15

38

Views

Difficulty with characterization of semisimplicity in terms of complements

Published on 03 Apr 2017 - 20:58

score 295 · Answer 6 · 2017-04-05 02:10:41

295

Views

criterion for direct product of H and G to be cyclic.

Published on 05 Apr 2017 - 2:10

score 299 · Answer 7 · 2017-04-06 09:29:30

299

Views

Structure of subgroups of direct products

Published on 06 Apr 2017 - 9:29

score 435 · Answer 8 · 2017-04-09 04:50:43

435

Views

Find a subgroup of $\mathbb{Z}_{12}\oplus \mathbb{Z}_{4}\oplus \mathbb{Z}_{15}$ of order 9

Published on 09 Apr 2017 - 4:50

score 178 · Answer 9 · 2023-01-31 15:42:35

178

Views

Does $G/K \cong H$ imply that $G \cong H\times K$ for normal $H,K$?

Published on 31 Jan 2023 - 15:42

score 76 · Answer 10 · 2026-02-23 06:36:33

76

Views

Exercise 3, Section 6.7 of Hoffman’s Linear Algebra

Published on 23 Feb 2026 - 6:36

score 110 · Answer 11 · 2026-03-25 19:04:47

110

Views

Unique factorization of free products of groups satisfying descending chain condition

Published on 25 Mar 2026 - 19:04

score 49 · Answer 12 · 2023-02-06 00:54:38

49

Views

Decomposition of Galois group into direct product using the main theorem

Published on 06 Feb 2023 - 0:54

score 75 · Answer 13 · 2023-02-26 11:18:05

75

Views

The dihedral group $D_n$ cannot be written as a product of two nontrivial groups

Published on 26 Feb 2023 - 11:18

score 254 · Answer 14 · 2023-02-26 23:46:07

254

Views

Let $G_1, G_2, ... , G_t$ be finite groups, and define $G = G_1 × G_2 × \cdots × G_t$. If $G$ is cyclic then $G_1,G_2,...,G_t$ must also be cyclic.

Published on 26 Feb 2023 - 23:46

score 72 · Answer 15 · 2026-03-25 07:44:59

72

Views

Size of maximal subgroups in the direct product of finite groups

Published on 25 Mar 2026 - 7:44

List Question

Non cyclic group of order 125 which has an element of order 25.

The zero divisors of $\Bbb Z/5\Bbb Z\times \Bbb Z/18\Bbb Z $.

Statement on an abelian group being isomorphic to a direct sum of cyclic groups

Possible chief factors of a group of order 336

Difficulty with characterization of semisimplicity in terms of complements

criterion for direct product of H and G to be cyclic.

Structure of subgroups of direct products

Find a subgroup of $\mathbb{Z}_{12}\oplus \mathbb{Z}_{4}\oplus \mathbb{Z}_{15}$ of order 9

Does $G/K \cong H$ imply that $G \cong H\times K$ for normal $H,K$?

Exercise 3, Section 6.7 of Hoffman’s Linear Algebra

Unique factorization of free products of groups satisfying descending chain condition

Decomposition of Galois group into direct product using the main theorem

The dihedral group $D_n$ cannot be written as a product of two nontrivial groups

Let $G_1, G_2, ... , G_t$ be finite groups, and define $G = G_1 × G_2 × \cdots × G_t$. If $G$ is cyclic then $G_1,G_2,...,G_t$ must also be cyclic.

Size of maximal subgroups in the direct product of finite groups

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