List questions from group-presentation

Published on 05 Dec 2018 - 10:23

134

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Show that $\mathbb{Z} = \langle a, b \mid a^{12} = b,\ ab = ba \rangle$ has dead end elements

Published on 24 Mar 2026 - 18:50

262

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Showing $\langle a,b\mid abab^{-1}\rangle$ and $ \langle c,d \mid c^2d^2\rangle$ are isomorphic.

Published on 05 Dec 2018 - 21:53

149

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Showing affine transformations group generated by $2x$ and $x+1$ is the Baumslag-Solitar group.

Published on 09 Dec 2018 - 21:52

157

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I am looking for a modern and thorough exposition for presentations of groups

Published on 16 Dec 2018 - 14:49

238

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Deriving the Discrete Heisenberg Group generators.

Published on 18 Dec 2018 - 15:45

96

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Why do generating sets need not contain the inverses of their elements?

Published on 18 Dec 2018 - 18:44

149

Views

Presentation of $A_5 \times \Bbb Z_2$.

Published on 30 Dec 2018 - 13:23

813

Views

Understanding semidirect product by constructing a non-abelian group of order $21$

Published on 31 Dec 2018 - 10:12

1.4k

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Can you make the triviality of $\langle a,b,c \mid aba^{-1} = b^2, bcb^{-1} = c^2, cac^{-1} = a^2 \rangle$ more trivial?

Published on 04 Jan 2019 - 4:13

206

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Finite Presentation of a subgroup

Published on 24 Mar 2026 - 1:47

408

Views

Quotient group of the dihedral group by $\langle r^2 \rangle.$

Published on 11 Jan 2019 - 17:51

1.1k

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Which of these numbers could be the exact number of elements of order $21$ in a group?

Published on 15 Jan 2019 - 14:56

86

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Derived subgroup of $\langle{x,y\,|\, x^p=y^{p^{n-1}}=1,\,{{x^{-1}}{yx}}={y^{1+p^{n-2}}}}\rangle$.

Published on 21 Mar 2026 - 21:01

582

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A proof that $\langle u,v\mid u^4=v^3=1, uv=v^2u^2\rangle$ defines the trivial group.

Published on 22 Mar 2026 - 4:00

List Question

Presentations of $D_8$ using permutations

Show that $\mathbb{Z} = \langle a, b \mid a^{12} = b,\ ab = ba \rangle$ has dead end elements

Showing $\langle a,b\mid abab^{-1}\rangle$ and $ \langle c,d \mid c^2d^2\rangle$ are isomorphic.

Showing affine transformations group generated by $2x$ and $x+1$ is the Baumslag-Solitar group.

I am looking for a modern and thorough exposition for presentations of groups

Deriving the Discrete Heisenberg Group generators.

Why do generating sets need not contain the inverses of their elements?

Presentation of $A_5 \times \Bbb Z_2$.

Understanding semidirect product by constructing a non-abelian group of order $21$

Can you make the triviality of $\langle a,b,c \mid aba^{-1} = b^2, bcb^{-1} = c^2, cac^{-1} = a^2 \rangle$ more trivial?

Finite Presentation of a subgroup

Quotient group of the dihedral group by $\langle r^2 \rangle.$

Which of these numbers could be the exact number of elements of order $21$ in a group?

Derived subgroup of $\langle{x,y\,|\, x^p=y^{p^{n-1}}=1,\,{{x^{-1}}{yx}}={y^{1+p^{n-2}}}}\rangle$.

A proof that $\langle u,v\mid u^4=v^3=1, uv=v^2u^2\rangle$ defines the trivial group.

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