Remarks on Two Generalizations of Normality of Subgroups

A subgroup H is said to be semi cover-avoiding in a group G if there is a chief series 1=G_0＜G_1＜…＜G_l=G such that for every i=1,…,l,either H covers G_j/G_(j-1) or H avoids G_j/G_(j-1).This paper shows that semi cover-avoidance is suitable to cover the both C-norrnality and the cover-avoidance property,and to characterize the solvability of groups by means of the maximal subgroups or Sylow subgroups.