List questions from combinatorial-group-theory

Published on 27 Dec 2012 - 18:58

166

Views

Determining $\langle a,b,c\mid 6a+9b+6c=0, 8a+12b+4c=0\rangle^{\operatorname{ab}}.$

Published on 26 Jan 2013 - 19:27

251

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How do I find $\left|\langle a,b\mid a^2=b^3=e\rangle\right|$?

Published on 22 Mar 2013 - 9:03

166

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Morphisms in the category of group presentations

Published on 30 Mar 2013 - 15:29

168

Views

Coset Enumeration: Defining Cosets

Published on 03 Aug 2020 - 8:40

120

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Checking Presentations in GAP

Published on 04 Aug 2020 - 15:11

63

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Determining group structure after computing homology: $\langle b,c \mid 2(b+c)=0, b+c=c+b \rangle.$

Published on 05 Aug 2020 - 19:48

62

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Prove the group defined by the following relations has eight elements and is not isomorphic to $\Delta_4$

Published on 25 Mar 2026 - 6:05

42

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Normal closure of a 2-subnormal subgroups

Published on 10 Aug 2020 - 14:31

170

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one-relator groups which are free-by-cyclic

Published on 24 Aug 2020 - 20:44

66

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Separating elements from relations over groups

Published on 25 Aug 2020 - 18:23

94

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What is the cardinality of the subgroup of $S_n$ generated by an $n$ cycle and a transposition.

Published on 27 Aug 2020 - 19:45

158

Views

Given a presentation $\langle x, y \mid x^n = y^2 = 1, xy = yx^2 \rangle$, what can we say about the order of the group?

Published on 01 Sep 2020 - 2:54

168

Views

finite groups are subgroups of the infinite one

Published on 02 Sep 2020 - 16:24

176

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What is the asymptotics of finite group presentation length?

Published on 13 Sep 2020 - 10:23

List Question

Calculating the index of a subgroup in a free group

Determining $\langle a,b,c\mid 6a+9b+6c=0, 8a+12b+4c=0\rangle^{\operatorname{ab}}.$

How do I find $\left|\langle a,b\mid a^2=b^3=e\rangle\right|$?

Morphisms in the category of group presentations

Coset Enumeration: Defining Cosets

Checking Presentations in GAP

Determining group structure after computing homology: $\langle b,c \mid 2(b+c)=0, b+c=c+b \rangle.$

Prove the group defined by the following relations has eight elements and is not isomorphic to $\Delta_4$

Normal closure of a 2-subnormal subgroups

one-relator groups which are free-by-cyclic

Separating elements from relations over groups

What is the cardinality of the subgroup of $S_n$ generated by an $n$ cycle and a transposition.

Given a presentation $\langle x, y \mid x^n = y^2 = 1, xy = yx^2 \rangle$, what can we say about the order of the group?

finite groups are subgroups of the infinite one

What is the asymptotics of finite group presentation length?

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