List questions from sylow-theory

Published on 01 Jan 2016 - 23:33

591

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Prove a finite group has non-normal Sylow p-subgroup of order p if $n_{p}\neq 1\pmod{p^2}$

Published on 02 Jan 2016 - 3:49

60

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Can a Simple Group possess this property?

Published on 27 Mar 2026 - 10:31

1.6k

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Show that a Sylow 2-subgroup of $A_5$ has exactly 5 conjugates

Published on 14 Jan 2016 - 17:13

414

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Inverse image of Sylow $p$-subgroup is Sylow $p$-subgroup

Published on 15 Jan 2016 - 11:00

1k

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Order of an Equivalence Class and the number of Coset.

Published on 15 Jan 2016 - 15:49

3.4k

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Prove that G has a normal Sylow p-subgroup

Published on 21 Jan 2016 - 23:09

1k

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Classify all groups of order $p^2q^2$ up to isomorphism

Published on 26 Mar 2026 - 19:00

1k

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Sylow subgroups of $\text{SL}_2(q)$.

Published on 26 Jan 2016 - 11:26

911

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$P$ is a Sylow subgroup of $G$ then $P$ is normal in $G$.

Published on 29 Jan 2016 - 17:25

52

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Prove that $g\in P$

Published on 06 Feb 2016 - 1:48

278

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Normalizers of subgroups of Sylow $p$-subgroups

Published on 09 Feb 2016 - 9:08

316

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Calculating $| \langle \bigcup_{i=1}^n P_i \rangle |$ where $P_i$ are Sylow subgroups of $G$

Published on 09 Feb 2016 - 20:44

160

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Sylow counting argument; prove G isomorphic to the direct product.

Published on 10 Feb 2016 - 14:56

104

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$G$ be a finite group and $f \in Aut (G)$ such that $f^3$ is identity and $f$ has unique fixed point , then any $p$-Sylow subgroup is normal?

Published on 10 Feb 2016 - 15:59

List Question

show that a Sylow p-group lies in the center of $G$

Prove a finite group has non-normal Sylow p-subgroup of order p if $n_{p}\neq 1\pmod{p^2}$

Can a Simple Group possess this property?

Show that a Sylow 2-subgroup of $A_5$ has exactly 5 conjugates

Inverse image of Sylow $p$-subgroup is Sylow $p$-subgroup

Order of an Equivalence Class and the number of Coset.

Prove that G has a normal Sylow p-subgroup

Classify all groups of order $p^2q^2$ up to isomorphism

Sylow subgroups of $\text{SL}_2(q)$.

$P$ is a Sylow subgroup of $G$ then $P$ is normal in $G$.

Prove that $g\in P$

Normalizers of subgroups of Sylow $p$-subgroups

Calculating $| \langle \bigcup_{i=1}^n P_i \rangle |$ where $P_i$ are Sylow subgroups of $G$

Sylow counting argument; prove G isomorphic to the direct product.

$G$ be a finite group and $f \in Aut (G)$ such that $f^3$ is identity and $f$ has unique fixed point , then any $p$-Sylow subgroup is normal?

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