List questions from finite-groups

Published on 15 Apr 2026 - 1:09

73

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a gap in the proof of statement 3.2.8 in Robinson's book

Published on 15 Apr 2026 - 14:32

526

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There is no surjective homomorphism from $S_4$ to $D_4$.

Published on 14 Apr 2026 - 19:46

297

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character table and nilpotency/solubility

Published on 12 Apr 2026 - 9:20

9.5k

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Find number of elements of order $p$ in group $G$ where $p$ is prime and $G$ has $m$ subgroups of order $p$

Published on 16 Apr 2026 - 0:31

481

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Finding all groups $H$ (up to isomorphism) such that there is a surjective homomorphism from $D_8$ to $H$

Published on 14 Apr 2026 - 10:59

276

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Let G and H be finite groups of the same order. If for any positive integer n, the number of elements in G having order n is the same as that in H

Published on 14 Apr 2026 - 18:22

495

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A reference for "a generalized quaternion group has a unique element of order 2".

Published on 15 Apr 2026 - 13:14

380

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Is "real character" means self-conjugate for representation of finite groups

Published on 11 Apr 2026 - 13:25

61

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Classifying groups such that $G \simeq \mathbb{Z}_3 \rtimes (\mathbb{Z}_2 \times \mathbb{Z}_2)$

Published on 13 Apr 2026 - 5:21

48

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Basic question about existene of subgroups of a particular order of an abelian group

Published on 17 Apr 2026 - 8:51

4.8k

Views

A finite $p$-group cannot be simple unless it has order $p$

Published on 13 Apr 2026 - 16:39

643

Views

Questions on Cosets.

Published on 09 Apr 2026 - 8:58

138

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Do distinct elements of $S_n$ afford distinct inner automorphisms of $S_n$?

Published on 16 Apr 2026 - 10:19

43

Views

$|$Inn$(S_2)|$ and $|$Aut$(S_2)|$

Published on 16 Apr 2026 - 10:03

List Question

Number of decompositions

a gap in the proof of statement 3.2.8 in Robinson's book

There is no surjective homomorphism from $S_4$ to $D_4$.

character table and nilpotency/solubility

Find number of elements of order $p$ in group $G$ where $p$ is prime and $G$ has $m$ subgroups of order $p$

Finding all groups $H$ (up to isomorphism) such that there is a surjective homomorphism from $D_8$ to $H$

Let G and H be finite groups of the same order. If for any positive integer n, the number of elements in G having order n is the same as that in H

A reference for "a generalized quaternion group has a unique element of order 2".

Is "real character" means self-conjugate for representation of finite groups

Classifying groups such that $G \simeq \mathbb{Z}_3 \rtimes (\mathbb{Z}_2 \times \mathbb{Z}_2)$

Basic question about existene of subgroups of a particular order of an abelian group

A finite $p$-group cannot be simple unless it has order $p$

Questions on Cosets.

Do distinct elements of $S_n$ afford distinct inner automorphisms of $S_n$?

$|$Inn$(S_2)|$ and $|$Aut$(S_2)|$

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