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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Item Type: | Article |
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Item Status: | Live Archive |
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 |
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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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