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Finite solvable group

221 bytes added, 00:58, 15 November 2008
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==Definition==
A [[defining ingredient::finite group]] is termed a '''finite solvable group''' if it satisfies the following equivalent conditions:
* # It is a [[defining ingredient::solvable group]]* # It is a [[defining ingredient::polycyclic group]]* # It has [[Sylow complement]]s for all prime divisors of the order of the group* # It has [[Hall subgroup]]s of all possible orders# All its composition factors (i.e., the quotient groups for any [[defining ingredient::composition series]] for the group) are cyclic groups of prime order.
==Relation with other properties==
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