On non-strictly simple groups

Abstract

Ascending series . Let G be a group and λ an ordinal number. An ascending series of G of type λ is a set of subgroups G α of G , defined for all α ≤ λ, and such that (i) G 0 = 1, G λ = G ; (ii) G α is a proper normal subgroup of G α+1 for all α < λ (iii) for all limit ordinals μ ≤ λ.