ON SOLVABILITY OF FINITE GROUPS WITH FEW NON-NORMAL SUBGROUPS

摘要

For a finite group G, let v(G) denote the number of conjugacy classes of non-normal subgroups of G and vc(G) denote the number of conjugacy classes of non-normal noncyclic subgroups of G. In this paper, we show that every finite group G satisfying v(G) 2|(G)| or vc(G) |(G)| is solvable, and for a finite nonsolvable group G, v(G)=2|(G)| +1 if and only if GA(5).