Some generalizations of normal series in infinite groups

Abstract

In this paper, we are concerned with certain generalizations of subnormal and ascendent (transfinitely subnormal) subgroups of a group. A subgroup A of a group G is called f-ascendent in G if there is a well ordered ascending complete series of subgroups of G , where for all α < λ, either G α ⊲ G α+1 or [G α+1 : G α ] < ∞. If such a series has finite length, A is called F -subnormal in G .