Nilpotent groups admitting an almost regular automorphism of order four

Makarenko, N. Yu. and Khukhro, E. I. (1996) Nilpotent groups admitting an almost regular automorphism of order four. Algebra and Logic, 35 (3). pp. 176-187. ISSN 0002-5232

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Abstract

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 � of order 4 having exactly m < � fixed points, then (a) the subgroup G, �2 contains a subgroup of m-bounded index in G, �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, �2 is nilpotent of m-bounded class (Theorem 1); (2) If a locally nilpotent periodic group G admits an automorphism � of order 4 having exactly m < � fixed points, then it contains a subgroup V of m-bounded index such that, for some m-bounded number f(m), the subgroup V, �2f(m), generated by all f(m)th powers of elements in V, �2

Additional Information:Supported by RFFR grant No. 94-01-00048 and by ISF grant NQ7000
Keywords:Algebra, Logic
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15750
Deposited On:19 Nov 2014 14:21

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