List questions from simple-groups

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Minimal degree representation of finite simple groups

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Prove a group of order $p(p+q)$ is not simple for primes $p$ and $q$ where $ p \geq q$.

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How to prove that a finite group of order $280$ is not simple?

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How to show that the intersection of 2 distinct p-Sylows (p prime) is the identity?

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How to prove that there is no simple group of order 10 000 000?

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A finite simple group with subgroup for every divisor of $|G|$ is abelian

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Show that every group of order $5865$ is cyclic

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$A_6$ does not have a subgroup of order $120$

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882

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Prove that there is no simple group of order $144$

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Could every finite simple group be related to a pair of Lie Groups?

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Simple groups in group theory 2

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A finite group of even order, whose $2$-Sylow subgroups are cyclic, is not simple.

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Can one prove that a group of order 150 is not simple using element counting?

Published on 12 Apr 2026 - 12:50

268

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For odd primes $p$, are finite groups with self-normalizing Sylow $p$-subgroups solvable?

Published on 13 Apr 2026 - 17:34

List Question

Groups for which all normal subgroups are perfect

Minimal degree representation of finite simple groups

Prove a group of order $p(p+q)$ is not simple for primes $p$ and $q$ where $ p \geq q$.

How to prove that a finite group of order $280$ is not simple?

How to show that the intersection of 2 distinct p-Sylows (p prime) is the identity?

How to prove that there is no simple group of order 10 000 000?

A finite simple group with subgroup for every divisor of $|G|$ is abelian

Show that every group of order $5865$ is cyclic

$A_6$ does not have a subgroup of order $120$

Prove that there is no simple group of order $144$

Could every finite simple group be related to a pair of Lie Groups?

Simple groups in group theory 2

A finite group of even order, whose $2$-Sylow subgroups are cyclic, is not simple.

Can one prove that a group of order 150 is not simple using element counting?

For odd primes $p$, are finite groups with self-normalizing Sylow $p$-subgroups solvable?

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