List questions from group-isomorphism

Published on 27 Mar 2026 - 1:45

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Why is $U(10)\not\approx U(12)$?

Published on 26 Jun 2015 - 6:12

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Group isomorphism exercise

Published on 03 Jul 2015 - 17:33

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Isomorphism between $H/H\cap N$ and $HN/N$

Published on 04 Jul 2015 - 9:08

50

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Find isomorphism for an operation

Published on 06 Jul 2015 - 4:13

476

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Show that $G/H\cong\mathbb{R}^*$.

Published on 27 Mar 2026 - 0:03

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Showing a Group $G$ is a Semidirect Product of $S_n$ and the Group of Diagonal Matrices with Entries $±1$.

Published on 29 Mar 2026 - 12:11

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If you check Groupisomorphism - does the operation, under which the Groups are closed, matter?

Published on 09 Jul 2015 - 13:40

144

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Let $G$ be a group of finite order, $H$ and $K$ subgroups so that $H \unlhd G$; $K \unlhd HK \unlhd G$ and $(|H|,|K|) = 1$. Show that $K \unlhd G$.

Published on 09 Jul 2015 - 18:41

376

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Dihedral subgroups of $S_4$

Published on 27 Mar 2026 - 10:44

319

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Dihedral Group question involving $D_{4n}$

Published on 27 Mar 2026 - 10:45

4.2k

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Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$

Published on 27 Mar 2026 - 16:25

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Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)

Published on 13 Jul 2015 - 19:19

291

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Do cycle graphs determine groups up to isomorphism?

Published on 27 Mar 2026 - 3:45

79

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show that $\varphi : H \to H /N$ is one-to-one correspondence using kernel

Published on 02 Apr 2026 - 0:22

List Question

Quotients of Solvable Groups are Solvable

Why is $U(10)\not\approx U(12)$?

Group isomorphism exercise

Isomorphism between $H/H\cap N$ and $HN/N$

Find isomorphism for an operation

Show that $G/H\cong\mathbb{R}^*$.

Showing a Group $G$ is a Semidirect Product of $S_n$ and the Group of Diagonal Matrices with Entries $±1$.

If you check Groupisomorphism - does the operation, under which the Groups are closed, matter?

Let $G$ be a group of finite order, $H$ and $K$ subgroups so that $H \unlhd G$; $K \unlhd HK \unlhd G$ and $(|H|,|K|) = 1$. Show that $K \unlhd G$.

Dihedral subgroups of $S_4$

Dihedral Group question involving $D_{4n}$

Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$

Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)

Do cycle graphs determine groups up to isomorphism?

show that $\varphi : H \to H /N$ is one-to-one correspondence using kernel

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