On self-normality and abnormality in the alternating groups

摘要

It is known that in a finite solvable group G, a subgroup H is abnormal if and only if every subgroup of G containing H is self-normalizing in G. Although, in general, the assumption of solvability cannot be dropped, in this paper we prove the theorem for the special case G = A(n) and H a second maximal intransitive subgroup of A(n).