Question

Normal subgroup generated by one element

score 383 · Answer 1 · 2022-07-15 13:36:46

383

Views

Normal subgroup generated by one element

Published on 15 Jul 2022 - 13:36

score 192 · Answer 2 · 2022-07-16 18:45:58

192

Views

Ways to guarantee that a group presentation defines a finite group when randomly generating group presentations

Published on 16 Jul 2022 - 18:45

score 109 · Answer 3 · 2022-08-11 15:33:38

109

Views

Does there exist a finitely generated, torsion group $G$ with a residually finite ascending HNN extension?

Published on 11 Aug 2022 - 15:33

score 108 · Answer 4 · 2022-08-30 14:09:52

108

Views

Classify the growth of poly-$\mathbb{Z}$ group

Published on 30 Aug 2022 - 14:09

score 87 · Answer 5 · 2022-09-03 17:59:17

87

Views

in a group presentation, any (ex-post) relation can be obtained as an elment of the normal closure of a (prior) "maximal" set of relators?

Published on 03 Sep 2022 - 17:59

score 112 · Answer 6 · 2022-09-07 13:32:34

112

Views

How many elements of the form $a^{m_1} b^{n_1} a^{m_2} b^{n_2} a^{m_3} b^{n_3}$ in $G:=\langle a,b \mid a^2, b^4, (ab)^3 \rangle?$

Published on 07 Sep 2022 - 13:32

score 137 · Answer 7 · 2022-09-22 15:24:43

137

Views

If group $G = \langle a,b\mid bab^{-1}=a^{-1}\rangle$, then how to verify every element can be written uniquely as form $a^ib^j$?

Published on 22 Sep 2022 - 15:24

score 38 · Answer 8 · 2022-09-26 16:05:36

38

Views

Length of a product of conjugates of an element in a free group

Published on 26 Sep 2022 - 16:05

score 50 · Answer 9 · 2022-09-29 22:05:15

50

Views

Equations on Free Groups

Published on 29 Sep 2022 - 22:05

score 90 · Answer 10 · 2022-10-03 18:54:36

90

Views

Probability that a random element of a group has order $2$

Published on 03 Oct 2022 - 18:54

score 85 · Answer 11 · 2022-10-22 18:16:08

85

Views

Birkhoff's characterization of varieties of groups

Published on 22 Oct 2022 - 18:16

score 77 · Answer 12 · 2026-03-26 06:14:02

77

Views

Classifying index 2 subgroups of $\langle a, b, c \mid ab = ba, c^2 = 1 \rangle$ up to isomorphism

Published on 26 Mar 2026 - 6:14

score 173 · Answer 13 · 2022-11-14 06:36:45

173

Views

Does every presentation correspond to a group?

Published on 14 Nov 2022 - 6:36

score 325 · Answer 14 · 2022-11-15 22:55:55

325

Views

Find the order of the group $G = \langle a,b \mid a^5 = b^4 = 1, aba^{-1}b = 1 \rangle$

Published on 15 Nov 2022 - 22:55

score 124 · Answer 15 · 2022-12-04 04:00:36

124

Views

Suppose $G=\left\langle x, y, t\mid x^7=y^7=t^3=1, txt^{-1}=x^2, tyt^{-1}=y\right\rangle$. Show that $y\in Z(G)$.

Published on 04 Dec 2022 - 4:00

List Question

Normal subgroup generated by one element

Ways to guarantee that a group presentation defines a finite group when randomly generating group presentations

Does there exist a finitely generated, torsion group $G$ with a residually finite ascending HNN extension?

Classify the growth of poly-$\mathbb{Z}$ group

in a group presentation, any (ex-post) relation can be obtained as an elment of the normal closure of a (prior) "maximal" set of relators?

How many elements of the form $a^{m_1} b^{n_1} a^{m_2} b^{n_2} a^{m_3} b^{n_3}$ in $G:=\langle a,b \mid a^2, b^4, (ab)^3 \rangle?$

If group $G = \langle a,b\mid bab^{-1}=a^{-1}\rangle$, then how to verify every element can be written uniquely as form $a^ib^j$?

Length of a product of conjugates of an element in a free group

Equations on Free Groups

Probability that a random element of a group has order $2$

Birkhoff's characterization of varieties of groups

Classifying index 2 subgroups of $\langle a, b, c \mid ab = ba, c^2 = 1 \rangle$ up to isomorphism

Does every presentation correspond to a group?

Find the order of the group $G = \langle a,b \mid a^5 = b^4 = 1, aba^{-1}b = 1 \rangle$

Suppose $G=\left\langle x, y, t\mid x^7=y^7=t^3=1, txt^{-1}=x^2, tyt^{-1}=y\right\rangle$. Show that $y\in Z(G)$.

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