List questions from group-isomorphism

Published on 21 Jan 2015 - 13:04

43

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Set of all distinct cosets of $\mathbb Z$ in $\mathbb R$ is not equipotent with the set of all distinct cosets of $2\mathbb Z$ in $\mathbb R$?

Published on 21 Jan 2015 - 14:14

706

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Presentation of a group isomorphic to $A_4$

Published on 27 Mar 2026 - 1:46

1.6k

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$\mathbb C$ isomorphism to $\mathbb{R} \times \mathbb{R}$ under multiplication

Published on 27 Jan 2015 - 21:51

4.9k

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When are two direct products of groups isomorphic?

Published on 28 Jan 2015 - 3:23

126

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$x=x^2$ in a sub group?

Published on 01 Apr 2026 - 12:46

411

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$(\mathbb Z_7^{*},\cdot)$ is isomorphic to $(\mathbb Z_6,+)$

Published on 31 Jan 2015 - 11:01

1.4k

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Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$

Published on 02 Feb 2015 - 12:36

195

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Determine whether the given map is a bijection and a homomorphism?

Published on 05 Feb 2015 - 4:08

100

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How to compute in $\Bbb{Z}_6 \rtimes \Bbb{Z}_2$?

Published on 29 Mar 2026 - 10:18

50

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Let $G$ be a group and let $\Phi\colon G \to G$ be an isomorphism. Define $H = \{ a \in G\ |\ \Phi(a) = a^{-1} \}$

Published on 05 Feb 2015 - 18:50

318

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Finding unique groups of C11 semidirect product C5

Published on 29 Mar 2026 - 10:18

68

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Show that the group of permutations of $\{1,2,3,4\}$ is equal to the product of it's subgroups...

Published on 29 Mar 2026 - 10:19

327

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Is this proof for $(\mathbb{Z},+) \ncong (\mathbb{Q},+)$ valid?

Published on 29 Mar 2026 - 22:26

233

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Two transformation groups of the hyperbolic plane are isomorphic?

Published on 30 Mar 2026 - 6:14

List Question

What are all the characteristic subgroups of $(\mathbb Q,+)$?

Set of all distinct cosets of $\mathbb Z$ in $\mathbb R$ is not equipotent with the set of all distinct cosets of $2\mathbb Z$ in $\mathbb R$?

Presentation of a group isomorphic to $A_4$

$\mathbb C$ isomorphism to $\mathbb{R} \times \mathbb{R}$ under multiplication

When are two direct products of groups isomorphic?

$x=x^2$ in a sub group?

$(\mathbb Z_7^{*},\cdot)$ is isomorphic to $(\mathbb Z_6,+)$

Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$

Determine whether the given map is a bijection and a homomorphism?

How to compute in $\Bbb{Z}_6 \rtimes \Bbb{Z}_2$?

Let $G$ be a group and let $\Phi\colon G \to G$ be an isomorphism. Define $H = \{ a \in G\ |\ \Phi(a) = a^{-1} \}$

Finding unique groups of C11 semidirect product C5

Show that the group of permutations of $\{1,2,3,4\}$ is equal to the product of it's subgroups...

Is this proof for $(\mathbb{Z},+) \ncong (\mathbb{Q},+)$ valid?

Two transformation groups of the hyperbolic plane are isomorphic?

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