Question

Let $G$ be a group isomorphic to $Z_{n_1} \oplus Z_{n_2} \oplus \cdots\oplus Z_{n_k}$.

score 109 · Answer 1 · 2023-09-08 08:06:33

109

Views

Let $G$ be a group isomorphic to $Z_{n_1} \oplus Z_{n_2} \oplus \cdots\oplus Z_{n_k}$.

Published on 08 Sep 2023 - 8:06

score 51 · Answer 2 · 2026-02-23 05:42:37

51

Views

One sided ideals of a semisimple ring.

Published on 23 Feb 2026 - 5:42

score 244 · Answer 3 · 2023-09-21 16:16:00

244

Views

Group action of direct product group $G \times H$ when groups $G$ and $H$ do not commute

Published on 21 Sep 2023 - 16:16

score 93 · Answer 4 · 2023-10-15 15:30:59

93

Views

$\mathrm{Hom}_A(\prod_i M_i, N) \cong \prod_i \mathrm{Hom}_A(M_i, N)$ and $\mathrm{Hom}_A (M, \bigoplus_i N_i) \cong \prod_i \mathrm{Hom}_A(M, N_i)$?

Published on 15 Oct 2023 - 15:30

score 37 · Answer 5 · 2023-10-20 10:49:13

37

Views

Internal direct product $\mathrm{H= \phi(N_1) \times \phi(N_2)}$

Published on 20 Oct 2023 - 10:49

score 52 · Answer 6 · 2023-10-26 09:01:12

52

Views

Direct product of groups are isomorphic, but factor groups are not isomorphic

Published on 26 Oct 2023 - 9:01

score 152 · Answer 7 · 2023-11-01 06:31:59

152

Views

Show that $G = HK$

Published on 01 Nov 2023 - 6:31

score 132 · Answer 8 · 2023-11-03 16:36:55

132

Views

Let $G_1, G_2$ be non-trivial groups. If $G_1 \times G_2$ is cyclic, then $G_1 \times G_2$ is finite.

Published on 03 Nov 2023 - 16:36

score 41 · Answer 9 · 2023-11-19 18:49:03

41

Views

External direct product realized as an internal direct product. What is the meaning of "realize"? Is my isomorphism correct?

Published on 19 Nov 2023 - 18:49

score 164 · Answer 10 · 2026-03-25 17:40:27

164

Views

How "exotic" are non-local directly irreducible modular group algebras?

Published on 25 Mar 2026 - 17:40

score 152 · Answer 11 · 2023-11-30 07:49:14

152

Views

When are all normal subgroups of a direct product of finite groups a direct product of normal subgroups?

Published on 30 Nov 2023 - 7:49

score 93 · Answer 12 · 2023-12-19 14:58:50

93

Views

Subgroups of index $2$ of $D_3 \times D_3$

Published on 19 Dec 2023 - 14:58

score 75 · Answer 13 · 2026-03-26 06:21:46

75

Views

Show that the direct product of structures satisfies a Horn sentence

Published on 26 Mar 2026 - 6:21

score 161 · Answer 14 · 2024-01-14 00:48:05

161

Views

"Let $G$ be a finite group with a normal subgroup $N\cong S_3$. Show there is $H\le G$ s.t. $G=N\times H$." Does this $=$ really mean $\cong$?

Published on 14 Jan 2024 - 0:48

score 242 · Answer 15 · 2026-02-23 13:38:39

242

Views

"Asymmetry" in the construction of products and coproducts in concrete categories

Published on 23 Feb 2026 - 13:38

List Question

Let $G$ be a group isomorphic to $Z_{n_1} \oplus Z_{n_2} \oplus \cdots\oplus Z_{n_k}$.

One sided ideals of a semisimple ring.

Group action of direct product group $G \times H$ when groups $G$ and $H$ do not commute

$\mathrm{Hom}_A(\prod_i M_i, N) \cong \prod_i \mathrm{Hom}_A(M_i, N)$ and $\mathrm{Hom}_A (M, \bigoplus_i N_i) \cong \prod_i \mathrm{Hom}_A(M, N_i)$?

Internal direct product $\mathrm{H= \phi(N_1) \times \phi(N_2)}$

Direct product of groups are isomorphic, but factor groups are not isomorphic

Show that $G = HK$

Let $G_1, G_2$ be non-trivial groups. If $G_1 \times G_2$ is cyclic, then $G_1 \times G_2$ is finite.

External direct product realized as an internal direct product. What is the meaning of "realize"? Is my isomorphism correct?

How "exotic" are non-local directly irreducible modular group algebras?

When are all normal subgroups of a direct product of finite groups a direct product of normal subgroups?

Subgroups of index $2$ of $D_3 \times D_3$

Show that the direct product of structures satisfies a Horn sentence

"Let $G$ be a finite group with a normal subgroup $N\cong S_3$. Show there is $H\le G$ s.t. $G=N\times H$." Does this $=$ really mean $\cong$?

"Asymmetry" in the construction of products and coproducts in concrete categories

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