A Note on Finite Groups Whose all of Subgroups are C-Normal

Abstract

-A subgroup H of a group G is said to be -normal in G if there exists a normal subgroup N of G such that HN=G and H∩N ≤ Core(H) where Core(H) is the largest normal subgroup of G contained in H . In this paper we consider finite p-groups of order at most p 4 where p is a prime and show that all of their subgroups are c-normal. Also we study some classes of finite groups whose all of subgroups are c-normal.