List questions from simple-groups

Published on 15 Dec 2014 - 9:38

145

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Fixed Spaces for Group Elements

Published on 25 Mar 2026 - 4:53

160

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Density of odd vs even group orders that are not forced to be simple by Sylow's Theorem

Published on 19 Dec 2014 - 10:02

908

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$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

Published on 23 Feb 2026 - 4:02

134

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There is no simple group of order $pq^2$.

Published on 02 Oct 2019 - 15:06

112

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Criterion for $PSL(2,q)$

Published on 03 Oct 2019 - 16:57

138

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Different attempt at proof of $A_n$ does not have a proper subgroup of index $< n$ for all $n \geq 5$

Published on 10 Oct 2019 - 17:35

77

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Number of Non-equivalent Generating Triples of Involutions in Finite Simple Groups

Published on 25 Mar 2026 - 7:46

99

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Is a direct limit of simple groups simple?

Published on 26 Oct 2019 - 17:16

84

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Show that a group of order $2^7 5^7$ cannot be simple

Published on 04 Nov 2019 - 19:06

408

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Proving that a finite simple group (order < 100) is either abelian or has order 60

Published on 05 Nov 2019 - 3:20

160

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Centralizer of a group of order 60 with $n_2=15,n_5=6,n_3=10$...

Published on 09 Nov 2019 - 18:35

305

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Using the fact that $A_n$ is simple for $n \geq 5$, prove that the only index 6 subgroups of $A_6$ and $S_6$ is $A_5$ and $S_5$ respectively

Published on 12 Nov 2019 - 3:38

957

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Prove there are no simple groups of even order $<500$ except orders $2$, $60$, $168$, and $360$.

Published on 13 Nov 2019 - 2:27

210

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Proof that in a simple group of order 168 the intersection of the normalizers of two distinct 7-sylows is of order 3

Published on 13 Nov 2019 - 14:03

List Question

What is a Simple Group?

Fixed Spaces for Group Elements

Density of odd vs even group orders that are not forced to be simple by Sylow's Theorem

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

There is no simple group of order $pq^2$.

Criterion for $PSL(2,q)$

Different attempt at proof of $A_n$ does not have a proper subgroup of index $< n$ for all $n \geq 5$

Number of Non-equivalent Generating Triples of Involutions in Finite Simple Groups

Is a direct limit of simple groups simple?

Show that a group of order $2^7 5^7$ cannot be simple

Proving that a finite simple group (order < 100) is either abelian or has order 60

Centralizer of a group of order 60 with $n_2=15,n_5=6,n_3=10$...

Using the fact that $A_n$ is simple for $n \geq 5$, prove that the only index 6 subgroups of $A_6$ and $S_6$ is $A_5$ and $S_5$ respectively

Prove there are no simple groups of even order $<500$ except orders $2$, $60$, $168$, and $360$.

Proof that in a simple group of order 168 the intersection of the normalizers of two distinct 7-sylows is of order 3

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