Question

If $G$ is isomorphic to $H_1\times\cdots\times H_n$, $H_i$ subgroup of $G$, then is $G$ the internal direct product of $H_1\cdots H_n$?

score 193 · Answer 1 · 2026-03-27 06:09:11

193

Views

If $G$ is isomorphic to $H_1\times\cdots\times H_n$, $H_i$ subgroup of $G$, then is $G$ the internal direct product of $H_1\cdots H_n$?

Published on 27 Mar 2026 - 6:09

score 145 · Answer 2 · 2015-10-08 21:58:06

145

Views

Two finitely generated abelian groups are isomorphic iff they are embedded in each other

Published on 08 Oct 2015 - 21:58

score 104 · Answer 3 · 2026-04-02 03:53:16

104

Views

Theorem 18 in Abstract Algebra by Dummit and Foote

Published on 02 Apr 2026 - 3:53

score 760 · Answer 4 · 2015-10-09 04:58:08

760

Views

How far can we go with group isomorphisms?

Published on 09 Oct 2015 - 4:58

score 1.2k · Answer 5 · 2026-03-27 01:47:38

1.2k

Views

Is the abelian nature of a group preserved under an isomorphism? Can we say the same thing for non-abelian groups?

Published on 27 Mar 2026 - 1:47

score 3k · Answer 6 · 2026-02-27 21:19:06

3k

Views

Showing that the groups (Q,+) and (Q⁺,*) are not isomorphic

Published on 27 Feb 2026 - 21:19

score 60 · Answer 7 · 2026-04-01 00:51:54

60

Views

Quotient isomorphism question.

Published on 01 Apr 2026 - 0:51

score 416 · Answer 8 · 2026-03-18 23:50:54

416

Views

Showing that the two groups are isomorphic

Published on 18 Mar 2026 - 23:50

score 1k · Answer 9 · 2026-03-27 07:32:59

1k

Views

A question about the composition series of two particular isomorphic groups

Published on 27 Mar 2026 - 7:32

score 54 · Answer 10 · 2015-10-13 00:32:12

54

Views

Find a group to which $A_4/V_{4}$ is isomorphic

Published on 13 Oct 2015 - 0:32

score 643 · Answer 11 · 2015-10-13 03:11:25

643

Views

Characteristic subgroups and automorphisms

Published on 13 Oct 2015 - 3:11

score 354 · Answer 12 · 2026-04-01 17:53:22

354

Views

Automorphisms of the Symmetric Group

Published on 01 Apr 2026 - 17:53

score 56 · Answer 13 · 2026-02-26 07:42:39

56

Views

Is $\mathbb{R}^\oplus \mathbb{R}^ \simeq \mathbb{C}^*$?

Published on 26 Feb 2026 - 7:42

score 75 · Answer 14 · 2015-10-13 23:25:02

75

Views

Is a group isomorphic to one of its realizations?

Published on 13 Oct 2015 - 23:25

score 95 · Answer 15 · 2015-10-14 14:23:17

95

Views

Questions about strong subgroups ($H < G$, $f(H)=H$ for all isomorphisms of $G$)

Published on 14 Oct 2015 - 14:23

List Question

If $G$ is isomorphic to $H_1\times\cdots\times H_n$, $H_i$ subgroup of $G$, then is $G$ the internal direct product of $H_1\cdots H_n$?

Two finitely generated abelian groups are isomorphic iff they are embedded in each other

Theorem 18 in Abstract Algebra by Dummit and Foote

How far can we go with group isomorphisms?

Is the abelian nature of a group preserved under an isomorphism? Can we say the same thing for non-abelian groups?

Showing that the groups (Q,+) and (Q⁺,*) are not isomorphic

Quotient isomorphism question.

Showing that the two groups are isomorphic

A question about the composition series of two particular isomorphic groups

Find a group to which $A_4/V_{4}$ is isomorphic

Characteristic subgroups and automorphisms

Automorphisms of the Symmetric Group

Is $\mathbb{R}^\oplus \mathbb{R}^ \simeq \mathbb{C}^*$?

Is a group isomorphic to one of its realizations?

Questions about strong subgroups ($H < G$, $f(H)=H$ for all isomorphisms of $G$)

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