✦ LIBER ✦

On Almost Fixed Point Free Automorphisms

✍ Scribed by A. Shalev

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 448 KB
Volume: 157
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1993.1100

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✦ Synopsis

Ideas from the theory of (p)-adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points. In particular we prove that the derived length of a finite (p)-group admitting an automorphism of order (p^{k}) with (p^{m}) fixed points is bounded in terms of (p, m, k). This extends a well-known result of Alperin dealing with the case (k=1). Some applications to soluble groups are also given. 1993 Academic Press. Inc

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