Abstract:

A subgroup H is said to be semi-cover-avoiding in a group G if there is a chief series 1=G₀1<…l=G such that for every j=1,2,…,l, either H covers Gj/Gj－1 or H  avoids  Gj/Gj－1. In this paper, some new necessary and sufficient conditions for a finite group G to be nilponent or supersolvable are given by using minimal subgroups and cyclic subgroups of order 4 with semi-cover-avoiding property in the group. Some known results are generalized. 

Key words: semi-cover-avoiding property; minimal subgroup; nilpotent group; supersolvble group; supersolvble embedding group