Classification of n􀀀characteristic autonilpotent groups

Given a group G, a subgroup AGn is defined as AGn = h[x; n] j x 2 G; 2 Aut(G)i: G is called n-characteristic group if AGn = 1 for some n 2 N. In the article we determine the structure of AGn in autonilpotent groups of class c 5 and among other results we prove G is an abelian 2-characteristic autonilpotent group of class 3 if and only if G C8.