List questions from finite-groups

Published on 13 Apr 2026 - 21:57

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Is a Sudoku a Cayley table for a group?

Published on 14 Apr 2026 - 13:41

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On Normality of a subgroup of a finite group

Published on 15 Apr 2026 - 12:06

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How to prove $\,{\rm order}(a^k) = n/\gcd(n,k)\,$ for $\,n={\rm order}(a)$?

Published on 16 Apr 2026 - 11:38

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Question from Herstein's Topics in Algebra on Sylow theory

Published on 14 Apr 2026 - 6:47

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Question from Herstein's Topics in Algebra on Sylow subgroups

Published on 15 Apr 2026 - 23:45

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Suppose G is a finite abelian group with a nontrivial subgroup H contained in every subgroup of G. Show that G is cyclic.

Published on 16 Apr 2026 - 15:55

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Does $B/A \cong D/C$ imply $C/A \cong D/B$ for fin. gen. free $\mathbb{Z}$-modules?

Published on 14 Apr 2026 - 13:19

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Application of Landau's theorem.

Published on 13 Apr 2026 - 17:13

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What can we get from (Brauer) character tables of a finite group?

Published on 14 Apr 2026 - 1:33

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How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?

Published on 09 Apr 2026 - 12:48

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Prove: Generator of cyclic group of order $n$ has $k^{th}$ root iff $\gcd(n,k) = 1$

Published on 13 Apr 2026 - 3:16

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Is the centralizer of a Subgroup abelian?

Published on 10 Apr 2026 - 16:22

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The order of the cyclic subgroups of $GL(3,q)$

Published on 15 Apr 2026 - 21:05

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Extensions of finite cyclic groups

Published on 09 Apr 2026 - 10:55

List Question

Show $\mathbb{Z}G$ is a noetherian ring for finite group $G$

Is a Sudoku a Cayley table for a group?

On Normality of a subgroup of a finite group

How to prove $\,{\rm order}(a^k) = n/\gcd(n,k)\,$ for $\,n={\rm order}(a)$?

Question from Herstein's Topics in Algebra on Sylow theory

Question from Herstein's Topics in Algebra on Sylow subgroups

Suppose G is a finite abelian group with a nontrivial subgroup H contained in every subgroup of G. Show that G is cyclic.

Does $B/A \cong D/C$ imply $C/A \cong D/B$ for fin. gen. free $\mathbb{Z}$-modules?

Application of Landau's theorem.

What can we get from (Brauer) character tables of a finite group?

How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?

Prove: Generator of cyclic group of order $n$ has $k^{th}$ root iff $\gcd(n,k) = 1$

Is the centralizer of a Subgroup abelian?

The order of the cyclic subgroups of $GL(3,q)$

Extensions of finite cyclic groups

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