Question

Does there exist a group that is both a free product and a direct product of nontrivial groups?

score 524 · Answer 1 · 2026-05-10 14:36:14

524

Views

Does there exist a group that is both a free product and a direct product of nontrivial groups?

Published on 10 May 2026 - 14:36

score 115 · Answer 2 · 2026-03-25 09:25:41

115

Views

Quaternion Group: Determine that $i^4 = 1$.

Published on 25 Mar 2026 - 9:25

score 231 · Answer 3 · 2026-03-25 09:28:55

231

Views

Can I conclude that my group is finitely generated, if it is a homomorphic image of a free-group on finitely many generators?

Published on 25 Mar 2026 - 9:28

score 135 · Answer 4 · 2026-05-10 16:13:06

135

Views

Proving the Free Abelian Group is Free Abelian...?

Published on 10 May 2026 - 16:13

score 79 · Answer 5 · 2026-04-10 23:29:41

79

Views

Reference for a result in group theory

Published on 10 Apr 2026 - 23:29

score 138 · Answer 6 · 2026-03-25 12:28:09

138

Views

If the inner automorphism group of a group $G$ is residually finite, then $G$ is residually finite group.

Published on 25 Mar 2026 - 12:28

score 296 · Answer 7 · 2026-03-25 09:29:59

296

Views

If we are handed the presentation $\langle i,j,k \mid i^2=j^2=k^2=ijk \rangle$ and nothing more, can we deduce that this is the quaternion group?

Published on 25 Mar 2026 - 9:29

score 199 · Answer 8 · 2026-03-25 10:53:42

199

Views

Fixed points of a group action on tree

Published on 25 Mar 2026 - 10:53

score 112 · Answer 9 · 2026-03-25 10:56:56

112

Views

Homomorphism condition for a subset of a group generates the whole group

Published on 25 Mar 2026 - 10:56

score 63 · Answer 10 · 2026-04-15 12:02:01

63

Views

A finite group $G$ and fixed $k\geq 1$ where for every $n\geq 1$, the $n$-direct product $G^n=G\times\dots\times G$ is $k$-generated?

Published on 15 Apr 2026 - 12:02

score 718 · Answer 11 · 2026-03-25 10:55:37

718

Views

How to show that $|D_{2n}| = 2n$ via the presentation?

Published on 25 Mar 2026 - 10:55

score 36 · Answer 12 · 2026-03-25 11:13:30

36

Views

Symmetrising the relations in a presentation of a group

Published on 25 Mar 2026 - 11:13

score 350 · Answer 13 · 2026-03-25 10:58:35

350

Views

Reduced word is uniquely written

Published on 25 Mar 2026 - 10:58

score 190 · Answer 14 · 2026-03-25 10:52:48

190

Views

$\infty$-ended subgroups of one-ended groups

Published on 25 Mar 2026 - 10:52

score 242 · Answer 15 · 2026-03-25 10:55:59

242

Views

Proving $G := \langle a, b, c \mid abc^{-1}a^{-1}, bcb \rangle$ is not isomorphic to $H := \langle a, b \rangle$

Published on 25 Mar 2026 - 10:55

List Question

Does there exist a group that is both a free product and a direct product of nontrivial groups?

Quaternion Group: Determine that $i^4 = 1$.

Can I conclude that my group is finitely generated, if it is a homomorphic image of a free-group on finitely many generators?

Proving the Free Abelian Group is Free Abelian...?

Reference for a result in group theory

If the inner automorphism group of a group $G$ is residually finite, then $G$ is residually finite group.

If we are handed the presentation $\langle i,j,k \mid i^2=j^2=k^2=ijk \rangle$ and nothing more, can we deduce that this is the quaternion group?

Fixed points of a group action on tree

Homomorphism condition for a subset of a group generates the whole group

A finite group $G$ and fixed $k\geq 1$ where for every $n\geq 1$, the $n$-direct product $G^n=G\times\dots\times G$ is $k$-generated?

How to show that $|D_{2n}| = 2n$ via the presentation?

Symmetrising the relations in a presentation of a group

Reduced word is uniquely written

$\infty$-ended subgroups of one-ended groups

Proving $G := \langle a, b, c \mid abc^{-1}a^{-1}, bcb \rangle$ is not isomorphic to $H := \langle a, b \rangle$

Trending Questions

Popular # Hahtags

Popular Questions