List questions from finite-groups

Published on 16 Apr 2026 - 4:51

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Visualizing $S_3 \rtimes D_4$

Published on 15 Apr 2026 - 6:53

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Group $G$ of order $n$. $b^m$ with $\gcd(m,n)=1$

Published on 16 Apr 2026 - 9:24

114

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Showing $\mathrm{PSL}(2,q)$ is perfect

Published on 15 Apr 2026 - 4:02

419

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Proof that field trace in $GF(2^k)$ maps half of the elements to 0 and the other half to 1.

Published on 16 Apr 2026 - 2:31

221

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What are the elements of $D_{4}/\{e,r_{180}\}$?

Published on 17 Apr 2026 - 6:40

53

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Existence of an element $g \in G$ of order $N$ in a finite group $G$ of order $N$

Published on 15 Apr 2026 - 11:08

1.3k

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Intersection of Maximal subgroups

Published on 11 Apr 2026 - 0:10

119

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A question from Isaac's book "Finite group theory" about Transfer theory

Published on 25 Apr 2026 - 22:43

53

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Do Mathieu Groups fit in a chain w.r.t. subgroup relation?

Published on 15 Apr 2026 - 7:05

65

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In $Z_p\times Z_p$, if the product of two group subsets of order $p$ and contain the identiy is the whole group, then one of them is a subgroup?

Published on 14 Apr 2026 - 13:33

112

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Use burnside's lemma to solve the follwing:

Published on 17 Apr 2026 - 10:40

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Embedding any finite group into $A_n$

Published on 15 Apr 2026 - 3:44

2.7k

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Finite abelian group contains an element with order equal to the lcm of the orders of its elements

Published on 11 Apr 2026 - 13:15

49

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Compute the order of a special group

Published on 15 Apr 2026 - 1:35

List Question

$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$

Visualizing $S_3 \rtimes D_4$

Group $G$ of order $n$. $b^m$ with $\gcd(m,n)=1$

Showing $\mathrm{PSL}(2,q)$ is perfect

Proof that field trace in $GF(2^k)$ maps half of the elements to 0 and the other half to 1.

What are the elements of $D_{4}/\{e,r_{180}\}$?

Existence of an element $g \in G$ of order $N$ in a finite group $G$ of order $N$

Intersection of Maximal subgroups

A question from Isaac's book "Finite group theory" about Transfer theory

Do Mathieu Groups fit in a chain w.r.t. subgroup relation?

In $Z_p\times Z_p$, if the product of two group subsets of order $p$ and contain the identiy is the whole group, then one of them is a subgroup?

Use burnside's lemma to solve the follwing:

Embedding any finite group into $A_n$

Finite abelian group contains an element with order equal to the lcm of the orders of its elements

Compute the order of a special group

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