Nilpotent groups admitting an almost regular automorphism of order four

<p>We consider locally nilpotent periodic groups admitting an almost regular automorphism of order 4. The following are results are proved: (1) If a locally nilpotent periodic group G admits an automorphism Ï? of order 4 having exactly m < â?? fixed points, then (a) the subgroup G, Ï?2 contains a subgroup of m-bounded index in G, Ï?2 which is nilpotent of m-bounded class, and (b) the group G contains a subgroup V of m-bounded index such that the subgroup V, Ï?2 is nilpotent of m-bounded class (Theorem 1); (2) If a locally nilpotent periodic group G admits an automorphism Ï? of order 4 having exactly m < â?? fixed points, then it contains a subgroup V of m-bounded index such that, for some m-bounded number f(m), the subgroup V, Ï?2f(m), generated by all f(m)th powers of elements in V, Ï?2</p>