List questions from finite-groups

Published on 11 Apr 2026 - 18:35

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Set of elements that do not generate $G$ with another one.

Published on 12 Apr 2026 - 3:31

131

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Name of group of order $p-\bigl(\frac ap\bigr)$ constructed from field $\Bbb Z_p$?

Published on 25 Mar 2026 - 14:36

138

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Show that there is no permutation $\sigma$ in $S_4$ that satisfies $(1\,2\,3\,4) \circ \sigma = \sigma \circ (1\,2) (3\,4) $

Published on 29 Mar 2026 - 5:12

100

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How to count the number of elements in the given set

Published on 11 Apr 2026 - 22:06

63

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Let $G$ be a group of order $360$. Let $A$ and $B$ be its Sylow-$2$ and Sylow-$3$ subgroups. Find the order of $A\cap B$

Published on 27 Mar 2026 - 23:14

159

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Orders of $GL_2$ and $SL_2$ over the field $\Bbb Z_p$

Published on 03 Apr 2026 - 23:03

110

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Check that $C$ is generated by $\sigma = (1 2 3 4)$ in symmetric group $S_4$.

Published on 29 Mar 2026 - 5:12

78

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In a finite group, if $e \notin A$, does $gA = A \implies g = e$?

Published on 12 Apr 2026 - 9:55

53

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Find the number of those $[a]\in \langle[5]\rangle$ such that $\gcd(a,6)=1$

Published on 30 Mar 2026 - 1:14

49

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Check whether or not $\{z \in \mathbb{C} \mid z^5=1\}$ is a group with respect to addition.

Published on 22 Feb 2020 - 12:00

46

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Obtain the order of each element of $\wp (S)$, where $S=\{1,2,3\}$

Published on 23 Feb 2020 - 7:18

256

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Abelian group of finite order

Published on 08 Apr 2026 - 18:36

47

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One-sided monoids and groups

Published on 06 Apr 2026 - 4:00

92

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A group is nilpotent if all of its local subgroups are subnormal

Published on 12 Apr 2026 - 0:00

List Question

Order of 2-generated finite group

Set of elements that do not generate $G$ with another one.

Name of group of order $p-\bigl(\frac ap\bigr)$ constructed from field $\Bbb Z_p$?

Show that there is no permutation $\sigma$ in $S_4$ that satisfies $(1\,2\,3\,4) \circ \sigma = \sigma \circ (1\,2) (3\,4) $

How to count the number of elements in the given set

Let $G$ be a group of order $360$. Let $A$ and $B$ be its Sylow-$2$ and Sylow-$3$ subgroups. Find the order of $A\cap B$

Orders of $GL_2$ and $SL_2$ over the field $\Bbb Z_p$

Check that $C$ is generated by $\sigma = (1 2 3 4)$ in symmetric group $S_4$.

In a finite group, if $e \notin A$, does $gA = A \implies g = e$?

Find the number of those $[a]\in \langle[5]\rangle$ such that $\gcd(a,6)=1$

Check whether or not $\{z \in \mathbb{C} \mid z^5=1\}$ is a group with respect to addition.

Obtain the order of each element of $\wp (S)$, where $S=\{1,2,3\}$

Abelian group of finite order

One-sided monoids and groups

A group is nilpotent if all of its local subgroups are subnormal

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