Question

Words in the alphabet of minimal generators of group

score 44 · Answer 1 · 2021-05-18 22:45:24

44

Views

Words in the alphabet of minimal generators of group

Published on 18 May 2021 - 22:45

score 154 · Answer 2 · 2021-05-21 12:04:46

154

Views

Suppose that group $G$ has a presentation $\langle a,b\mid a^{4} = b^{7} = 1, ab=ba^{3}\rangle$

Published on 21 May 2021 - 12:04

score 72 · Answer 3 · 2021-05-28 21:23:47

72

Views

Is the symmetric group over 8 items, $S_8$, presented by $\langle x, y \mid x^2 = e, y^8 = e, (xy)^7 = e \rangle$?

Published on 28 May 2021 - 21:23

score 606 · Answer 4 · 2021-06-01 03:11:07

606

Views

Let $G$ be a group and if $a,b \in G$ such that $a^4 =e$ and $a^2 b=ba$ then prove that $a=e$

Published on 01 Jun 2021 - 3:11

score 72 · Answer 5 · 2021-06-01 14:24:37

72

Views

Let $F$ be freely generated by $\{a, b, c\}$. Prove that $F/N$ is free with basis $aN, bN$, where $N$ is the normal subgroup of $F$ generated by $c$

Published on 01 Jun 2021 - 14:24

score 125 · Answer 6 · 2021-06-04 02:52:17

125

Views

Two-generator, one-relator presentations of the free group

Published on 04 Jun 2021 - 2:52

score 45 · Answer 7 · 2021-06-04 15:16:50

45

Views

Is $\langle S \rangle / \operatorname{nc}(T) \simeq \langle S \setminus T \rangle$, where $T \subseteq S$?

Published on 04 Jun 2021 - 15:16

score 93 · Answer 8 · 2021-06-05 21:32:04

93

Views

Show finite $\langle x,y,z,t\rangle$ with relations $y^x=y^2$, $z^y=z^2$, $t^z=t^2$, $x^t=x^2$ is trivial.

Published on 05 Jun 2021 - 21:32

score 117 · Answer 9 · 2021-06-07 13:41:53

117

Views

Finitely presented group with all rank $2$ subgroups not finitely presented?

Published on 07 Jun 2021 - 13:41

score 82 · Answer 10 · 2021-06-13 15:37:01

82

Views

Finding special presentations for finite groups

Published on 13 Jun 2021 - 15:37

score 81 · Answer 11 · 2026-03-27 04:34:18

81

Views

Defining a map on a subgroup of a free group

Published on 27 Mar 2026 - 4:34

score 78 · Answer 12 · 2021-07-01 08:07:41

78

Views

Finding a group with minimal generators and then a subgroup generated by these as an index two normal subgroup.

Published on 01 Jul 2021 - 8:07

score 224 · Answer 13 · 2026-03-25 22:02:36

224

Views

Every free group admits a fixed-point-free involution automorphism

Published on 25 Mar 2026 - 22:02

score 336 · Answer 14 · 2021-07-12 16:48:34

336

Views

Writing $G/[G, G]$ as a direct product of cyclic groups

Published on 12 Jul 2021 - 16:48

score 43 · Answer 15 · 2021-07-12 17:49:42

43

Views

Is there a systematic way to find the center of a finitely-presented, finite $p$ group?

Published on 12 Jul 2021 - 17:49

List Question

Words in the alphabet of minimal generators of group

Suppose that group $G$ has a presentation $\langle a,b\mid a^{4} = b^{7} = 1, ab=ba^{3}\rangle$

Is the symmetric group over 8 items, $S_8$, presented by $\langle x, y \mid x^2 = e, y^8 = e, (xy)^7 = e \rangle$?

Let $G$ be a group and if $a,b \in G$ such that $a^4 =e$ and $a^2 b=ba$ then prove that $a=e$

Let $F$ be freely generated by $\{a, b, c\}$. Prove that $F/N$ is free with basis $aN, bN$, where $N$ is the normal subgroup of $F$ generated by $c$

Two-generator, one-relator presentations of the free group

Is $\langle S \rangle / \operatorname{nc}(T) \simeq \langle S \setminus T \rangle$, where $T \subseteq S$?

Show finite $\langle x,y,z,t\rangle$ with relations $y^x=y^2$, $z^y=z^2$, $t^z=t^2$, $x^t=x^2$ is trivial.

Finitely presented group with all rank $2$ subgroups not finitely presented?

Finding special presentations for finite groups

Defining a map on a subgroup of a free group

Finding a group with minimal generators and then a subgroup generated by these as an index two normal subgroup.

Every free group admits a fixed-point-free involution automorphism

Writing $G/[G, G]$ as a direct product of cyclic groups

Is there a systematic way to find the center of a finitely-presented, finite $p$ group?

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