Ivan Shishkin, Birch Grove

pp-subgroup

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Revision 1008

8/6/2026, 9:36:55 PM · Sequoia

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1A $p$-subgroup of a [[Finite group|finite group]] $G$ is a [[Subgroup|subgroup]] $H$ of $G$ which is a $p$[[$p$-group|-group]], that is, whose [[Order of a finite group|order]] is a power of $p$:
1Let $p$ be a [[Prime number|prime number]]. A $p$-subgroup of a [[Finite group|finite group]] $G$ is a [[Subgroup|subgroup]] $H$ of $G$ which is a $p$[[$p$-group|-group]], that is, whose [[Order of a finite group|order]] is a power of $p$:
2$$|H|=p^{k}$$
3for some $k\geq 0$

Revision 1006

8/6/2026, 9:34:31 PM · Sequoia

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Revision 963

8/6/2026, 12:52:10 PM · Ancient Tree

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1A $p$-subgroup of a [[Finite group|finite group]] $G$ is a [[Subgroup|subgroup]] $H$ of $G$ which is a $p$-group, that is, whose [[Order of a finite group|order]] is a power of $p$:
1A $p$-subgroup of a [[Finite group|finite group]] $G$ is a [[Subgroup|subgroup]] $H$ of $G$ which is a $p$[[$p$-group|-group]], that is, whose [[Order of a finite group|order]] is a power of $p$:
2$$|H|=p^{k}$$
3for some $k\geq 0$

Revision 961

8/6/2026, 12:49:22 PM · Ancient Tree

Concept created

A $p$-subgroup of a [[Finite group|finite group]] $G$ is a [[Subgroup|subgroup]] $H$ of $G$ which is a $p$-group, that is, whose [[Order of a finite group|order]] is a power of $p$:
$$|H|=p^{k}$$
for some $k\geq 0$