Question

$G= \langle a, b : a^{7} = b^{3} = 1,\ b^{-1}ab = a^{2} \rangle$ and commutator group

score 56 · Answer 1 · 2026-03-26 04:14:38

56

Views

$G= \langle a, b : a^{7} = b^{3} = 1,\ b^{-1}ab = a^{2} \rangle$ and commutator group

Published on 26 Mar 2026 - 4:14

score 179 · Answer 2 · 2026-03-22 10:23:17

179

Views

Are the terms of the derived series of finitely generated groups finitely normally generated?

Published on 22 Mar 2026 - 10:23

score 379 · Answer 3 · 2026-02-23 19:17:11

379

Views

Heisenberg group modulo prime

Published on 23 Feb 2026 - 19:17

score 167 · Answer 4 · 2020-07-21 14:51:20

167

Views

Trying to prove any relation between elements of a group can be derived from the relations in the presentation of the group

Published on 21 Jul 2020 - 14:51

score 174 · Answer 5 · 2026-03-26 04:20:02

174

Views

Compute the order of each of the elements in $D_6$ where $D_{6}=\left\langle r, s \mid r^{3}=s^{2}=1, r s=s r^{-1}\right\rangle$

Published on 26 Mar 2026 - 4:20

score 873 · Answer 6 · 2016-07-09 12:11:54

873

Views

How to write the commutator subgroup in terms of the generators of the group?

Published on 09 Jul 2016 - 12:11

score 97 · Answer 7 · 2016-07-17 17:26:21

97

Views

If $G$ is a finitely presented group then is the commutator of $G$ isomorphic to the commutator of $F$ mod the relations?

Published on 17 Jul 2016 - 17:26

score 113 · Answer 8 · 2026-03-26 04:14:47

113

Views

How to write $\Bbb Z_q\rtimes\Bbb Z_p$ as $\langle a,b\mid a^p=b^q=1,aba^{-1}=b^{i_0}\rangle?$

Published on 26 Mar 2026 - 4:14

score 75 · Answer 9 · 2016-08-10 17:14:23

75

Views

For a Group $G$ with$S\subseteq G$, when does $ \left\langle S \right\rangle $ equal the normal closure of $S$?

Published on 10 Aug 2016 - 17:14

score 701 · Answer 10 · 2026-03-26 04:53:40

701

Views

Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.

Published on 26 Mar 2026 - 4:53

score 132 · Answer 11 · 2026-03-26 09:30:50

132

Views

Finitely presented monoid with non-solvable word problem

Published on 26 Mar 2026 - 9:30

score 307 · Answer 12 · 2026-03-25 23:53:05

307

Views

Normal and non-normal subgroups of a finite $p$-group

Published on 25 Mar 2026 - 23:53

score 198 · Answer 13 · 2026-03-26 06:34:53

198

Views

How to show $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle$ is presentation of an infinite group?

Published on 26 Mar 2026 - 6:34

score 504 · Answer 14 · 2016-09-22 08:10:58

504

Views

Presentations of Semidirect Product of Groups

Published on 22 Sep 2016 - 8:10

score 145 · Answer 15 · 2026-03-25 16:02:08

145

Views

Commutative diagram of semidirect products

Published on 25 Mar 2026 - 16:02

List Question

$G= \langle a, b : a^{7} = b^{3} = 1,\ b^{-1}ab = a^{2} \rangle$ and commutator group

Are the terms of the derived series of finitely generated groups finitely normally generated?

Heisenberg group modulo prime

Trying to prove any relation between elements of a group can be derived from the relations in the presentation of the group

Compute the order of each of the elements in $D_6$ where $D_{6}=\left\langle r, s \mid r^{3}=s^{2}=1, r s=s r^{-1}\right\rangle$

How to write the commutator subgroup in terms of the generators of the group?

If $G$ is a finitely presented group then is the commutator of $G$ isomorphic to the commutator of $F$ mod the relations?

How to write $\Bbb Z_q\rtimes\Bbb Z_p$ as $\langle a,b\mid a^p=b^q=1,aba^{-1}=b^{i_0}\rangle?$

For a Group $G$ with$S\subseteq G$, when does $ \left\langle S \right\rangle $ equal the normal closure of $S$?

Trying to prove that $H=\langle a,b:a^{3}=b^{3}=(ab)^{3}=1\rangle$ is a group of infinite order.

Finitely presented monoid with non-solvable word problem

Normal and non-normal subgroups of a finite $p$-group

How to show $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle$ is presentation of an infinite group?

Presentations of Semidirect Product of Groups

Commutative diagram of semidirect products

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