Question

Why is $\langle a,b,c,d\mid abcda^{-1}b^{-1}c^{-1}d^{-1}\rangle\cong \langle a,b,c,d\mid aba^{-1}b^{-1}cdc^{-1}d^{-1}\rangle$?

score 403 · Answer 1 · 2026-03-26 05:55:58

403

Views

Why is $\langle a,b,c,d\mid abcda^{-1}b^{-1}c^{-1}d^{-1}\rangle\cong \langle a,b,c,d\mid aba^{-1}b^{-1}cdc^{-1}d^{-1}\rangle$?

Published on 26 Mar 2026 - 5:55

score 100 · Answer 2 · 2023-02-06 02:39:28

100

Views

Is the following presentation for $D_8$ a valid presentation?

Published on 06 Feb 2023 - 2:39

score 80 · Answer 3 · 2026-03-25 06:09:47

80

Views

Unique factorization of elements in $SL_2(\mathbb{Z})$

Published on 25 Mar 2026 - 6:09

score 89 · Answer 4 · 2026-03-26 04:53:39

89

Views

Minimal presentation of non-abelian group of order $p^3$ and exponent $p^2$

Published on 26 Mar 2026 - 4:53

score 226 · Answer 5 · 2026-03-26 06:00:53

226

Views

A basic question on group presentation

Published on 26 Mar 2026 - 6:00

score 94 · Answer 6 · 2023-02-26 23:34:20

94

Views

What is the order of a group given three generators, $a^2=b^3=c^4=1$ and $cb=ac$

Published on 26 Feb 2023 - 23:34

score 124 · Answer 7 · 2023-03-20 12:12:06

124

Views

Definition of Presentation of Group in Dummit’s Abstract Algebra

Published on 20 Mar 2023 - 12:12

score 60 · Answer 8 · 2026-03-26 05:56:19

60

Views

relationship between Torsion and Relations

Published on 26 Mar 2026 - 5:56

score 79 · Answer 9 · 2023-04-26 09:23:17

79

Views

Maximal quotient group of direct product

Published on 26 Apr 2023 - 9:23

score 133 · Answer 10 · 2026-03-26 07:35:38

133

Views

Prove that the group $G = \langle x, y \, \mid \, x^2=y^3=(xy)^3=1 \rangle$ is finite.

Published on 26 Mar 2026 - 7:35

score 48 · Answer 11 · 2023-04-29 06:01:25

48

Views

a typo about free groups in Dummit's Abstract Algebra

Published on 29 Apr 2023 - 6:01

score 82 · Answer 12 · 2026-03-26 07:35:33

82

Views

The abelianization of $\langle t_1,...,t_n | t_1^2...t_n^2 \rangle$ is $\mathbb{Z}^{n-1} \oplus \mathbb{Z}/2\mathbb{Z}$

Published on 26 Mar 2026 - 7:35

score 80 · Answer 13 · 2023-05-07 16:44:54

80

Views

Find three subgroups of $QD16$ of order $8$, and find the isomorphism type of each group.

Published on 07 May 2023 - 16:44

score 47 · Answer 14 · 2026-03-26 07:39:06

47

Views

Order of the group $\langle x, y \mid x^3 = y^2 = (xy)^3 = 1\rangle$.

Published on 26 Mar 2026 - 7:39

score 71 · Answer 15 · 2026-03-25 17:42:21

71

Views

Are the only finite orders of elements of this group in $\{p^k\mid k\in\Bbb N\cup\{0\}\}?$

Published on 25 Mar 2026 - 17:42

List Question

Why is $\langle a,b,c,d\mid abcda^{-1}b^{-1}c^{-1}d^{-1}\rangle\cong \langle a,b,c,d\mid aba^{-1}b^{-1}cdc^{-1}d^{-1}\rangle$?

Is the following presentation for $D_8$ a valid presentation?

Unique factorization of elements in $SL_2(\mathbb{Z})$

Minimal presentation of non-abelian group of order $p^3$ and exponent $p^2$

A basic question on group presentation

What is the order of a group given three generators, $a^2=b^3=c^4=1$ and $cb=ac$

Definition of Presentation of Group in Dummit’s Abstract Algebra

relationship between Torsion and Relations

Maximal quotient group of direct product

Prove that the group $G = \langle x, y \, \mid \, x^2=y^3=(xy)^3=1 \rangle$ is finite.

a typo about free groups in Dummit's Abstract Algebra

The abelianization of $\langle t_1,...,t_n | t_1^2...t_n^2 \rangle$ is $\mathbb{Z}^{n-1} \oplus \mathbb{Z}/2\mathbb{Z}$

Find three subgroups of $QD16$ of order $8$, and find the isomorphism type of each group.

Order of the group $\langle x, y \mid x^3 = y^2 = (xy)^3 = 1\rangle$.

Are the only finite orders of elements of this group in $\{p^k\mid k\in\Bbb N\cup\{0\}\}?$

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