List questions from sylow-theory

Published on 05 Mar 2018 - 15:48

268

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Sylow subgroup is normal iff subgroups generated are p-subgroups

Published on 05 Mar 2018 - 16:12

36

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(T/F): $(a \ b \ c),(a' \ b' \ c')\in A_5\Rightarrow \exists \omega\in A_5:(a \ b \ c)=\omega (a' \ b' \ c')\omega^{-1}$

Published on 10 Mar 2018 - 17:53

605

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No simple group of order $1,000,000$

Published on 22 Mar 2026 - 0:12

39

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On the Sylow 2-subgroup of a finite group

Published on 22 Mar 2026 - 18:35

54

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Group of order $545$ is cyclic?

Published on 22 Mar 2026 - 4:08

223

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$G$ is a group of order $pq$ and $P_q$ and $P_p$ are Sylow subgroups...

Published on 22 Mar 2026 - 18:25

124

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Let $G$ be a group of order $2^3 7^2 11$

Published on 22 Mar 2026 - 16:24

346

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Converse Lagrange Theorem for groups with cyclic Sylow subgroups

Published on 25 Mar 2018 - 9:52

124

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Does Frattini argument hold for subnormal subgroup?

Published on 29 Mar 2018 - 5:52

80

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Groups without using Sylow

Published on 20 Mar 2026 - 7:41

546

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Generalization of the Sylow theorem(part I)

Published on 22 Mar 2026 - 14:28

28

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A normal minimal subgroup in a Sylow 2-subgroup

Published on 03 Apr 2018 - 12:31

141

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Show that $|N_G(\langle x\rangle)|$ is a multiple of $5^27$, where $|G|=35^2*7$ and $x\in C$, a cyclic subgroup of order 35.

Published on 04 Apr 2018 - 3:16

410

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Why all subgroups of order 2 of Alternating group A5 are conjugate?

Published on 04 Apr 2018 - 11:37

List Question

Sylow p-subgroup is normal if and only if it is a characteristic subgroup

Sylow subgroup is normal iff subgroups generated are p-subgroups

(T/F): $(a \ b \ c),(a' \ b' \ c')\in A_5\Rightarrow \exists \omega\in A_5:(a \ b \ c)=\omega (a' \ b' \ c')\omega^{-1}$

No simple group of order $1,000,000$

On the Sylow 2-subgroup of a finite group

Group of order $545$ is cyclic?

$G$ is a group of order $pq$ and $P_q$ and $P_p$ are Sylow subgroups...

Let $G$ be a group of order $2^3 7^2 11$

Converse Lagrange Theorem for groups with cyclic Sylow subgroups

Does Frattini argument hold for subnormal subgroup?

Groups without using Sylow

Generalization of the Sylow theorem(part I)

A normal minimal subgroup in a Sylow 2-subgroup

Show that $|N_G(\langle x\rangle)|$ is a multiple of $5^27$, where $|G|=35^2*7$ and $x\in C$, a cyclic subgroup of order 35.

Why all subgroups of order 2 of Alternating group A5 are conjugate?

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