Question

Find non-trivial groups $G, H$ such that $G \cong H \times G$

score 77 · Answer 1 · 2022-06-27 12:34:29

77

Views

Find non-trivial groups $G, H$ such that $G \cong H \times G$

Published on 27 Jun 2022 - 12:34

score 79 · Answer 2 · 2022-07-04 01:34:50

79

Views

Is one-to-one-ness and operation preservation sufficient to prove an isomorphism between two finite groups with identical cardinality?

Published on 04 Jul 2022 - 1:34

score 195 · Answer 3 · 2022-07-04 22:25:50

Amount of Isomorphisms Between Two Cyclic Groups of Identical Order is equal to the amount of Automorphisms of one of the cyclic groups

score 64 · Answer 4 · 2022-07-05 15:56:10

64

Views

Prove for any $[a] \in \mathbb{Z}^\times_n$ multiplication by $[a]$ defines an automorphism $\alpha_{[a]}: \mathbb{Z}_n \to \mathbb{Z}_n$

Published on 05 Jul 2022 - 15:56

score 205 · Answer 5 · 2026-04-07 04:55:58

205

Views

Why is $\{1,-1,i,-i\}$ isomorphic to the cyclic group $C_4$?

Published on 07 Apr 2026 - 4:55

score 349 · Answer 6 · 2026-04-08 19:41:52

349

Views

Show $S_7$ is isomorphic to the subgroup of all those elements of $S_8$ which leave the number $5$ fixed

Published on 08 Apr 2026 - 19:41

score 231 · Answer 7 · 2026-04-08 09:36:56

231

Views

About Group Isomorphism Kernel

Published on 08 Apr 2026 - 9:36

score 93 · Answer 8 · 2026-03-29 12:41:10

93

Views

Prove that the free monoid is unique (up to isomorphism)

Published on 29 Mar 2026 - 12:41

score 89 · Answer 9 · 2022-07-11 14:49:44

89

Views

Are $([0,1),+_{\text{mod}1})$ and $(\mathbb{R}_{>0},\cdot)$ isomorphic?

Published on 11 Jul 2022 - 14:49

score 122 · Answer 10 · 2022-07-15 06:59:39

122

Views

For which groups can an isomorphism between subgroups always be lifted to an automorphism?

Published on 15 Jul 2022 - 6:59

score 281 · Answer 11 · 2022-07-15 16:46:22

281

Views

Left action and group automorphism

Published on 15 Jul 2022 - 16:46

score 92 · Answer 12 · 2022-07-16 01:53:36

92

Views

Prove any group of order $p^2$ is isomorphic to either $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_p \times \mathbb{Z}_p$

Published on 16 Jul 2022 - 1:53

score 62 · Answer 13 · 2026-04-05 18:21:56

62

Views

Homomorphism between two groups

Published on 05 Apr 2026 - 18:21

score 128 · Answer 14 · 2026-04-05 18:26:25

128

Views

Isomorphism to the group of all infinite binary sequences.

Published on 05 Apr 2026 - 18:26

score 132 · Answer 15 · 2026-03-30 08:37:31

132

Views

Morphism of free groups that induces isomorphism on abelianizations

Published on 30 Mar 2026 - 8:37

List Question

Find non-trivial groups $G, H$ such that $G \cong H \times G$

Is one-to-one-ness and operation preservation sufficient to prove an isomorphism between two finite groups with identical cardinality?

Amount of Isomorphisms Between Two Cyclic Groups of Identical Order is equal to the amount of Automorphisms of one of the cyclic groups

Prove for any $[a] \in \mathbb{Z}^\times_n$ multiplication by $[a]$ defines an automorphism $\alpha_{[a]}: \mathbb{Z}_n \to \mathbb{Z}_n$

Why is $\{1,-1,i,-i\}$ isomorphic to the cyclic group $C_4$?

Show $S_7$ is isomorphic to the subgroup of all those elements of $S_8$ which leave the number $5$ fixed

About Group Isomorphism Kernel

Prove that the free monoid is unique (up to isomorphism)

Are $([0,1),+_{\text{mod}1})$ and $(\mathbb{R}_{>0},\cdot)$ isomorphic?

For which groups can an isomorphism between subgroups always be lifted to an automorphism?

Left action and group automorphism

Prove any group of order $p^2$ is isomorphic to either $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_p \times \mathbb{Z}_p$

Homomorphism between two groups

Isomorphism to the group of all infinite binary sequences.

Morphism of free groups that induces isomorphism on abelianizations

Trending Questions

Popular # Hahtags

Popular Questions