# Finite solvable group

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Revision as of 23:57, 21 February 2008 by Vipul (talk | contribs) (New page: {{finite group property}} ==Definition== A finite group is termed a '''finite solvable group''' if it satisfies the following equivalent conditions: * It is a solvable group * I...)

This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)

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## Definition

A finite group is termed a **finite solvable group** if it satisfies the following equivalent conditions:

- It is a solvable group
- It is a polycyclic group
- It has Sylow complements for all prime divisors of the order of the group
- It has Hall subgroups of all possible orders