Some sufficient conditions for a group to be nilpotent

Abstract

Let () G=G0>G>G>... >G=I be chain of subgroups of the group G. Following Klou]nine [1], we define the stability group of the chain (1) to be the group A of 11 uutomorphisms of G such that (2) x holds for ll x e G_ nd for each i 1, 2, m.