Abstract:

Based on a wellknown theorem which asserts that groups of odd order are solvable, this paper deals with the relationships between the semi-2-cover-avoiding property of subgroups and the solvability of finite groups with the help of the methods of induction and minimal counterexamples, with a series of sufficient and necessary conditions for a finite group to be solvable. It is shown that the semi-2-cover-avoiding property can characterize solvable groups as the normality does nilpotent groups.

Key words: maximal subgroup, semi-2-cover-avoiding property, solvable group