G is p-solvable if G satisies one of the following conditions: (1) there exists a normal subgroup N of G such that p |(|G / N|,|N|): (2) for every irreducible complex character x with p |x(1) or x(1) is a power of a fixed prime q.

• 如果G满足下述条件之一；那么G是P~-可解的:(1)存在正规子群N使p|(|G/N|；|N|); (2)对G的每个不可约复特征标x；或者P|x(1)；或者x(1)是一固定素数q的方幂.