List questions from group-isomorphism

Published on 14 Mar 2022 - 6:41

68

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Why is $(\mathbb{Z}\oplus \mathbb{Z}\oplus \mathbb{Z})/(a_1+a_2+a_3=0)\cong \mathbb{Z}$?

Published on 16 Mar 2022 - 9:10

169

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Can the direct product of nontrivial groups $A\times B$ ever be isomorphic to a free group?

Published on 30 Mar 2026 - 6:48

97

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Isomorphism Between Two Subgroups of $GL_2(\mathbb{F})$

Published on 23 Mar 2022 - 15:54

293

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Prove that ${\rm Inn}(S_n)$ isomorphic to $S_n.$

Published on 05 Apr 2026 - 7:18

412

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If $G,H$ are finite groups, then $G\times G\cong H \times H$ implies $G \cong H$

Published on 28 Mar 2026 - 20:09

257

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What is wrong with my proof of group order?

Published on 25 Mar 2022 - 15:06

137

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Proof verification of Dummit and Foote exercise 1.6.24

Published on 29 Mar 2026 - 13:27

55

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Is $\operatorname{Hol}(D_4)$ isomorphic to a familiar group?

Published on 23 Feb 2026 - 0:28

179

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When is $D_n\approx\operatorname{Aut}(D_n)$?

Published on 29 Mar 2026 - 13:27

187

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Do isomorphic groups have the same number of Sylow $p$-subgroups?

Published on 29 Mar 2022 - 15:23

132

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Galois group $G$ where every element fixes a root is trivial

Published on 01 Apr 2022 - 4:58

96

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Show the function between the dihedral groups is well defined

Published on 08 Apr 2026 - 22:58

910

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Do the groups $\operatorname{SL}$, $\operatorname{PGL}$, and $\operatorname{PSL}$ over a field $K$ always have the same automorphism group?

Published on 01 Apr 2026 - 20:06

117

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The given function $\phi$ is not an isomorphism because it is not surjective. But it's not injective either, right?

Published on 30 Mar 2026 - 15:43

List Question

A question on group isomorphism between $(\Bbb{R},+) $ and $(\Bbb{C}, +) $ .

Why is $(\mathbb{Z}\oplus \mathbb{Z}\oplus \mathbb{Z})/(a_1+a_2+a_3=0)\cong \mathbb{Z}$?

Can the direct product of nontrivial groups $A\times B$ ever be isomorphic to a free group?

Isomorphism Between Two Subgroups of $GL_2(\mathbb{F})$

Prove that ${\rm Inn}(S_n)$ isomorphic to $S_n.$

If $G,H$ are finite groups, then $G\times G\cong H \times H$ implies $G \cong H$

What is wrong with my proof of group order?

Proof verification of Dummit and Foote exercise 1.6.24

Is $\operatorname{Hol}(D_4)$ isomorphic to a familiar group?

When is $D_n\approx\operatorname{Aut}(D_n)$?

Do isomorphic groups have the same number of Sylow $p$-subgroups?

Galois group $G$ where every element fixes a root is trivial

Show the function between the dihedral groups is well defined

Do the groups $\operatorname{SL}$, $\operatorname{PGL}$, and $\operatorname{PSL}$ over a field $K$ always have the same automorphism group?

The given function $\phi$ is not an isomorphism because it is not surjective. But it's not injective either, right?

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