List questions from sylow-theory

Published on 07 Nov 2014 - 13:57

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Every $p$-subgroup is contained in one $p$-Sylow subgroup?

Published on 07 Nov 2014 - 16:23

3.6k

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Every finite $p$-group is solvable

Published on 08 Nov 2014 - 13:34

1.9k

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Show that a group of order $180$ is not simple.

Published on 11 Nov 2014 - 21:56

435

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Isomorphism type of two quotient groups of $G=\mathbb{Z}^\times_{16}$

Published on 25 Mar 2026 - 22:06

133

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Why is $G$ abelian?

Published on 15 Nov 2014 - 15:56

608

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Sylow $p$-subgroup of $GL_{n}(\mathbb{F}_{q})$

Published on 16 Nov 2014 - 21:31

6.4k

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Groups of order 24.

Published on 18 Nov 2014 - 23:40

773

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For any group $G$, $|G/Z(G)| \neq 91$.

Published on 26 Nov 2014 - 17:20

2.4k

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Which are the nine Sylow $2$-subgroups of $S_3 \times S_3$? What is the only Sylow $3$-subgroup of $S_3 \times S_3$? And the most important...Why?

Published on 27 Nov 2014 - 1:26

3.7k

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Intersection of all $p$-Sylow subgroups is normal

Published on 27 Nov 2014 - 22:40

225

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maximum number of elements of order 5 in a group of order 80

Published on 28 Nov 2014 - 0:42

1.2k

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Question involving Sylow's Thm for $|G|=245$

Published on 29 Nov 2014 - 18:43

92

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Check: Find all the Sylow $3$-subgroups of $A_4$.

Published on 30 Nov 2014 - 22:24

1k

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Group of order 7.11.17 is cyclic

Published on 25 Mar 2026 - 17:22

List Question

T/F questions on $p$-Sylow subgroups and normalizer

Every $p$-subgroup is contained in one $p$-Sylow subgroup?

Every finite $p$-group is solvable

Show that a group of order $180$ is not simple.

Isomorphism type of two quotient groups of $G=\mathbb{Z}^\times_{16}$

Why is $G$ abelian?

Sylow $p$-subgroup of $GL_{n}(\mathbb{F}_{q})$

Groups of order 24.

For any group $G$, $|G/Z(G)| \neq 91$.

Which are the nine Sylow $2$-subgroups of $S_3 \times S_3$? What is the only Sylow $3$-subgroup of $S_3 \times S_3$? And the most important...Why?

Intersection of all $p$-Sylow subgroups is normal

maximum number of elements of order 5 in a group of order 80

Question involving Sylow's Thm for $|G|=245$

Check: Find all the Sylow $3$-subgroups of $A_4$.

Group of order 7.11.17 is cyclic

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