List questions from finite-groups

Published on 13 Apr 2026 - 5:58

130

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Prove that $H$ is normal.

Published on 10 Apr 2026 - 19:04

240

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To find $|Aut(K_{4})| = |Aut(\mathbb{Z}_{2} \times \mathbb{Z}_{2})|$

Published on 14 Apr 2026 - 16:30

252

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A finite non-abelian $p$-group contains at least an element of order $p^2$

Published on 16 Apr 2026 - 8:23

147

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Permutations of polynomials

Published on 11 Apr 2026 - 23:50

138

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Isomorphism between tensor products of abelian groups

Published on 16 Apr 2026 - 15:21

342

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Abelian group of order $p^m$ having only one subgroup of order $p^{m-1}$

Published on 17 Apr 2026 - 5:09

1.4k

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Give three examples of groups of order 120, no two of which are isomorphic.

Published on 15 Apr 2026 - 20:37

733

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Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.

Published on 16 Apr 2026 - 14:59

378

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Maximal subgroups of $PSL(2,q)$

Published on 14 Apr 2026 - 7:19

79

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Group Theory about proving there exists m,n such that $(x ∗ y)^{−1}= y^m ∗ x^n$

Published on 15 Apr 2026 - 19:18

38

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$SL_2(q)$ is isomorphic to $SU_2(q)$.

Published on 14 Apr 2026 - 3:02

128

Views

Orthonormal basis in group ring necessarily characters?

Published on 14 Apr 2026 - 18:50

22

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$p$-groups as specific central quotients

Published on 12 Apr 2026 - 8:22

118

Views

Lengths of $p$-central $p$-series

Published on 16 Apr 2026 - 15:19

List Question

If $|G|=7 \times 11 \times 19$, then $G$ is abelian.

Prove that $H$ is normal.

To find $|Aut(K_{4})| = |Aut(\mathbb{Z}_{2} \times \mathbb{Z}_{2})|$

A finite non-abelian $p$-group contains at least an element of order $p^2$

Permutations of polynomials

Isomorphism between tensor products of abelian groups

Abelian group of order $p^m$ having only one subgroup of order $p^{m-1}$

Give three examples of groups of order 120, no two of which are isomorphic.

Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.

Maximal subgroups of $PSL(2,q)$

Group Theory about proving there exists m,n such that $(x ∗ y)^{−1}= y^m ∗ x^n$

$SL_2(q)$ is isomorphic to $SU_2(q)$.

Orthonormal basis in group ring necessarily characters?

$p$-groups as specific central quotients

Lengths of $p$-central $p$-series

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