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 -groups and  -groups
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(Definition)
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Let $\pi$ be a set of primes. A torsion group $G$ is called a $\pi$ -group if each prime dividing the order of an element of $G$ is in $\pi$ and a $\pi'$ -group if none of them are. Typically, if $\pi$ is a singleton $\pi=\{p\}$ , we write $p$ -group and $p'$ -group for these.
Remark. If $G$ is finite, then $G$ is a $\pi$ -group if every prime dividing $|G|$ is in $\pi$ .
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" -groups and  -groups" is owned by Algeboy. [ full author list (3) | owner history (2) ]
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| Also defines: |
-group, -group |
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Cross-references: finite, singleton, order, torsion group, primes
There are 3 references to this entry.
This is version 6 of  -groups and  -groups, born on 2002-12-20, modified 2009-02-20.
Object id is 3797, canonical name is PiGroupsAndPiGroups.
Accessed 4602 times total.
Classification:
| AMS MSC: | 20D20 (Group theory and generalizations :: Abstract finite groups :: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure) | | | 20F50 (Group theory and generalizations :: Special aspects of infinite or finite groups :: Periodic groups; locally finite groups) |
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Pending Errata and Addenda
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