Question

The Grigorchuk group does not satisfy the Tits Alternative: A Reference Request.

score 142 · Answer 1 · 2019-10-08 14:54:31

142

Views

The Grigorchuk group does not satisfy the Tits Alternative: A Reference Request.

Published on 08 Oct 2019 - 14:54

score 85 · Answer 2 · 2019-10-23 19:58:39

85

Views

Finding a normal form for the group given by $\langle a,t| t^{-1}at = a^{2}\rangle.$

Published on 23 Oct 2019 - 19:58

score 113 · Answer 3 · 2026-03-07 03:26:50

113

Views

Prove that the relation $\leq$ on the braid group $B_n$ is anti symmetric.

Published on 07 Mar 2026 - 3:26

score 408 · Answer 4 · 2019-11-09 00:12:15

408

Views

Non-trivial semidirect product $\mathbb Z_3\rtimes Q_8$ is isomorphic to dicyclic group of order $24$

Published on 09 Nov 2019 - 0:12

score 405 · Answer 5 · 2019-11-14 17:34:18

405

Views

Show that a group $G$ is finitely generated if and only if it is a quotient of a free group on a finite set of letters

Published on 14 Nov 2019 - 17:34

score 108 · Answer 6 · 2019-11-20 13:06:18

108

Views

Need to understand the statement: "Symmetry group of all complete graphs is vertex transitive."

Published on 20 Nov 2019 - 13:06

score 162 · Answer 7 · 2019-11-22 18:53:38

162

Views

Can any relation in the group be derived from the relations in the presentation?

Published on 22 Nov 2019 - 18:53

score 472 · Answer 8 · 2019-11-23 21:57:21

472

Views

A Normal subgroup of a free group generated via a fixed integer

Published on 23 Nov 2019 - 21:57

score 215 · Answer 9 · 2019-11-24 21:01:36

215

Views

Show $\langle x,y|x^3=y^3=(xy)^3=1\rangle$ is isomophic to $A\rtimes\langle t\rangle$, where $t^3=1$ and $A=\langle a\rangle\times\langle b\rangle$.

Published on 24 Nov 2019 - 21:01

score 24 · Answer 10 · 2026-03-22 15:55:26

24

Views

Is there some sort of formula for $[F_n : V_{\{x^4\}}(F_n)]$?

Published on 22 Mar 2026 - 15:55

score 113 · Answer 11 · 2019-12-06 08:16:03

113

Views

Generating an infinite group with more than one commutative generator of finite order

Published on 06 Dec 2019 - 8:16

score 106 · Answer 12 · 2019-12-14 01:00:49

106

Views

Effect of Generators and Relations on a Finite Group's Order

Published on 14 Dec 2019 - 1:00

score 178 · Answer 13 · 2019-12-20 19:06:03

178

Views

Will Todd-Coxeter algorithm always determine the order of the group?

Published on 20 Dec 2019 - 19:06

score 57 · Answer 14 · 2019-12-25 15:05:46

57

Views

Show that $\langle x,y,z \rangle$ has order $42$ for $x,y,z$ with given properties

Published on 25 Dec 2019 - 15:05

score 109 · Answer 15 · 2019-12-27 22:07:30

109

Views

Can Higman's embedding theorem be generalised that way?

Published on 27 Dec 2019 - 22:07

List Question

The Grigorchuk group does not satisfy the Tits Alternative: A Reference Request.

Finding a normal form for the group given by $\langle a,t| t^{-1}at = a^{2}\rangle.$

Prove that the relation $\leq$ on the braid group $B_n$ is anti symmetric.

Non-trivial semidirect product $\mathbb Z_3\rtimes Q_8$ is isomorphic to dicyclic group of order $24$

Show that a group $G$ is finitely generated if and only if it is a quotient of a free group on a finite set of letters

Need to understand the statement: "Symmetry group of all complete graphs is vertex transitive."

Can any relation in the group be derived from the relations in the presentation?

A Normal subgroup of a free group generated via a fixed integer

Show $\langle x,y|x^3=y^3=(xy)^3=1\rangle$ is isomophic to $A\rtimes\langle t\rangle$, where $t^3=1$ and $A=\langle a\rangle\times\langle b\rangle$.

Is there some sort of formula for $[F_n : V_{\{x^4\}}(F_n)]$?

Generating an infinite group with more than one commutative generator of finite order

Effect of Generators and Relations on a Finite Group's Order

Will Todd-Coxeter algorithm always determine the order of the group?

Show that $\langle x,y,z \rangle$ has order $42$ for $x,y,z$ with given properties

Can Higman's embedding theorem be generalised that way?

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