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Sylow p-subgroup
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(Definition)
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If $(G,*)$ is a group then any subgroup of order $p^a$ for any integer a is called a p-subgroup. If $|G|=p^am$ , where $p\nmid m$ then any subgroup $S$ of $G$ with $|S|=p^a$ is a Sylow p-subgroup. We use ${\rm Syl_p}(G)$ for the set of
Sylow p-groups of $G$ .
More generally, if $G$ is any group (not necessarily finite), a Sylow p-subgroup is a maximal $p$ -subgroup of $G$ .
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"Sylow p-subgroup" is owned by Henry.
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Cross-references: maximal, finite, p-groups, p-subgroup, integer, order, subgroup, group
There are 17 references to this entry.
This is version 5 of Sylow p-subgroup, born on 2002-07-22, modified 2007-08-20.
Object id is 3181, canonical name is SylowPSubgroup.
Accessed 11619 times total.
Classification:
| AMS MSC: | 20D20 (Group theory and generalizations :: Abstract finite groups :: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure) |
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Pending Errata and Addenda
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