Question

Say we have a presentation of a finite group. Does adding additional relations to the presentation always decrease the size of the group?

score 230 · Answer 1 · 2016-03-24 15:34:46

230

Views

Say we have a presentation of a finite group. Does adding additional relations to the presentation always decrease the size of the group?

Published on 24 Mar 2016 - 15:34

score 343 · Answer 2 · 2016-03-29 04:07:46

343

Views

presentation of the symmetric group via transpositions fixing one element

Published on 29 Mar 2016 - 4:07

score 143 · Answer 3 · 2016-04-01 15:51:26

143

Views

Expository reference on group presentations

Published on 01 Apr 2016 - 15:51

score 58 · Answer 4 · 2016-04-02 11:53:08

58

Views

Construction of a group where nonempty words of small length are not equal to the identity element

Published on 02 Apr 2016 - 11:53

score 517 · Answer 5 · 2016-04-05 15:35:22

517

Views

Universal cover of a CW complex corresponding to an identification space

Published on 05 Apr 2016 - 15:35

score 70 · Answer 6 · 2026-03-07 10:56:25

70

Views

Let $G=\langle X\mid R\rangle$ and $H=\langle X\mid S\rangle$. If $R\subseteq S$, the $H$ is isomorphic to a quotient of $G$.

Published on 07 Mar 2026 - 10:56

score 27 · Answer 7 · 2016-04-13 21:07:08

27

Views

A function vanishing on the subgroup generated by relations defines a linear function.

Published on 13 Apr 2016 - 21:07

score 36 · Answer 8 · 2016-04-17 03:33:20

36

Views

By mapping the generators $s_{i}$ into $S_{n}$ appropriately, find a well-defined epimorphism $\theta :G_{n}\rightarrow S_{n}$ .

Published on 17 Apr 2016 - 3:33

score 851 · Answer 9 · 2016-04-18 16:37:34

851

Views

For every group $G$ there is a $2$-dimensional cell complex $X_G$ with $\pi_1(X_G)\cong G$.

Published on 18 Apr 2016 - 16:37

score 84 · Answer 10 · 2016-04-22 14:31:05

84

Views

Do these two permutations generate $A_n$?

Published on 22 Apr 2016 - 14:31

score 4.7k · Answer 11 · 2016-04-23 09:24:33

4.7k

Views

Determining the presentation matrix for a module

Published on 23 Apr 2016 - 9:24

score 120 · Answer 12 · 2026-03-18 23:52:09

120

Views

Proving a group $G$ with presentation $\langle a,b\mid ab\rangle$ is isomorphic to $\Bbb Z$.

Published on 18 Mar 2026 - 23:52

score 95 · Answer 13 · 2016-05-06 07:18:49

95

Views

Von Dyck groups that are conjugated.

Published on 06 May 2016 - 7:18

score 118 · Answer 14 · 2016-05-15 20:19:09

118

Views

Quotient of $G= \left\langle a, b \ \middle|\ a^4, b^2=a^4, aba=b \right\rangle$ by $\langle a^2 \rangle$

Published on 15 May 2016 - 20:19

score 57 · Answer 15 · 2016-05-18 10:49:10

57

Views

How can I identify the following group of three generators

Published on 18 May 2016 - 10:49

List Question

Say we have a presentation of a finite group. Does adding additional relations to the presentation always decrease the size of the group?

presentation of the symmetric group via transpositions fixing one element

Expository reference on group presentations

Construction of a group where nonempty words of small length are not equal to the identity element

Universal cover of a CW complex corresponding to an identification space

Let $G=\langle X\mid R\rangle$ and $H=\langle X\mid S\rangle$. If $R\subseteq S$, the $H$ is isomorphic to a quotient of $G$.

A function vanishing on the subgroup generated by relations defines a linear function.

By mapping the generators $s_{i}$ into $S_{n}$ appropriately, find a well-defined epimorphism $\theta :G_{n}\rightarrow S_{n}$ .

For every group $G$ there is a $2$-dimensional cell complex $X_G$ with $\pi_1(X_G)\cong G$.

Do these two permutations generate $A_n$?

Determining the presentation matrix for a module

Proving a group $G$ with presentation $\langle a,b\mid ab\rangle$ is isomorphic to $\Bbb Z$.

Von Dyck groups that are conjugated.

Quotient of $G= \left\langle a, b \ \middle|\ a^4, b^2=a^4, aba=b \right\rangle$ by $\langle a^2 \rangle$

How can I identify the following group of three generators

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