Hall subgroups and pi-separable groups

[摘要] Let G be a finite group and a a set of primes. In this paper, some new criteria for pi-separable groups and pi-solvable groups in terms of Hall subgroups are proved. The main results are the following: Theorem. G is a pi-separable group if and only if (1) G satisfies E-pi and E-pi'; (2) G satisfies E-pi boolean OR(q) and E-pi'boolean OR(p) for all p is an element of pi, q is an element of pi'. Theorem. G is a pi-separable group if and only if (1) G satisfies E-pi and E-pi'; (2) G satisfies E-p,E- q for all p is an element of pi and q is an element of pi'. (C) 1997 Academic Press.

[发布日期] 1997-09-15