List questions from group-presentation

Published on 26 Oct 2022 - 18:27

41

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Are there any 2-generated groups that are terminally 1-generated?

Published on 27 Oct 2022 - 17:11

77

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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

174

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Does every presentation correspond to a group?

Published on 28 Mar 2026 - 2:09

326

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

Published on 28 Mar 2026 - 2:07

134

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Question on the definition of the Dihedral groups

Published on 29 Mar 2026 - 18:03

127

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Universal Property of the Free Abelian Group on $S$.

Published on 20 Nov 2022 - 18:39

113

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A monoid presentation with invertible generators is a group presentation

Published on 29 Mar 2026 - 17:31

133

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Show $A_5 \cong \langle x,y \mid x^5,y^2,(xy)^3\rangle$

Published on 30 Nov 2022 - 17:34

189

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A group presentation given by the Collatz sequence of a fixed $n$. Has this been studied before?

Published on 01 Dec 2022 - 0:51

97

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Are group presentations useful in studying the pure math of a group as a whole?

Published on 02 Dec 2022 - 0:47

125

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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 28 Mar 2026 - 2:06

73

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Amalgamated product of finite cyclic groups is not abelian

Published on 15 Dec 2022 - 13:44

104

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Prove that $\langle a,b\mid ab=ba^n\rangle$ is not isomorphic to $\langle a,b\mid ab=ba^{n'}\rangle$ when $n\neq n'$

Published on 29 Mar 2026 - 14:02

131

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Step in a proof that $G:=\langle x,y \mid x^n,y^2, (xy)^2\rangle$ is isomorphic to the dihedral group $D_n$

Published on 29 Mar 2026 - 18:10

List Question

A certain subgroup is isomorphic to Klein group

Are there any 2-generated groups that are terminally 1-generated?

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 $G = \langle a,b \mid a^5 = b^4 = 1, aba^{-1}b = 1 \rangle$

Question on the definition of the Dihedral groups

Universal Property of the Free Abelian Group on $S$.

A monoid presentation with invertible generators is a group presentation

Show $A_5 \cong \langle x,y \mid x^5,y^2,(xy)^3\rangle$

A group presentation given by the Collatz sequence of a fixed $n$. Has this been studied before?

Are group presentations useful in studying the pure math of a group as a whole?

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 $y\in Z(G)$.

Amalgamated product of finite cyclic groups is not abelian

Prove that $\langle a,b\mid ab=ba^n\rangle$ is not isomorphic to $\langle a,b\mid ab=ba^{n'}\rangle$ when $n\neq n'$

Step in a proof that $G:=\langle x,y \mid x^n,y^2, (xy)^2\rangle$ is isomorphic to the dihedral group $D_n$

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