List questions from finite-groups

Published on 25 Mar 2026 - 12:53

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If a finite group $G$ of order $n$ has at most one subgroup of each order $d\mid n$, then $G$ is cyclic

Published on 15 Apr 2026 - 8:11

42

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Order of the $p^s$-torsion subgroup of $C_{p^r}$ for some prime $p$

Published on 13 Apr 2026 - 23:59

321

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Do all finite groups contain an odd number of elements?

Published on 14 Apr 2026 - 22:09

36

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Reference Request : Representation Theory Of Finite p-groups

Published on 25 Mar 2026 - 23:56

321

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Showing $f(h)=g^{-1}h^{-1}gh$ for any $g \in G, h\in H$ where $H$ is normal subgroup of $G$.

Published on 12 Apr 2026 - 22:59

390

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Classification of groups of order 66

Published on 15 Apr 2026 - 6:29

176

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Is the product of two soluble groups always soluble??

Published on 11 Apr 2026 - 0:27

73

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A doubt about Theorem 14 in textbook Algebra by Saunders MacLane and Garrett Birkhoff

Published on 14 Apr 2026 - 23:54

523

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Why do partitions correspond to irreps in $S_n$?

Published on 10 Apr 2026 - 13:10

31

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Extend the direct product representation of a subgroup

Published on 13 Apr 2026 - 1:07

119

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Orders of subgroups in decomposition of abelian groups

Published on 10 Apr 2026 - 4:45

40

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Is there any condition for groups that have subgroups of order of all divisors of its order?

Published on 15 Apr 2026 - 0:57

850

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Let $F$ be a finite field. Then the multiplicative group $(F \setminus \{0\}, \cdot)$ is cyclic

Published on 14 Apr 2026 - 23:03

69

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Generators of $O_8^+(2):\mathbb Z_2$

Published on 26 Mar 2026 - 4:16

List Question

Finitely Presented Group of order $p^4$

If a finite group $G$ of order $n$ has at most one subgroup of each order $d\mid n$, then $G$ is cyclic

Order of the $p^s$-torsion subgroup of $C_{p^r}$ for some prime $p$

Do all finite groups contain an odd number of elements?

Reference Request : Representation Theory Of Finite p-groups

Showing $f(h)=g^{-1}h^{-1}gh$ for any $g \in G, h\in H$ where $H$ is normal subgroup of $G$.

Classification of groups of order 66

Is the product of two soluble groups always soluble??

A doubt about Theorem 14 in textbook Algebra by Saunders MacLane and Garrett Birkhoff

Why do partitions correspond to irreps in $S_n$?

Extend the direct product representation of a subgroup

Orders of subgroups in decomposition of abelian groups

Is there any condition for groups that have subgroups of order of all divisors of its order?

Let $F$ be a finite field. Then the multiplicative group $(F \setminus \{0\}, \cdot)$ is cyclic

Generators of $O_8^+(2):\mathbb Z_2$

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