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On Almost Regular Automorphisms of Finite p-Groups

✍ Scribed by A. Jaikin-Zapirain

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 143 KB
Volume: 153
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1999.1911

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✦ Synopsis

In this paper we prove that there are functions f ( p, m, n) and h(m) such that any finite p-group with an automorphism of order p n , whose centralizer has p m points, has a subgroup of derived length h(m) and index f ( p, m, n). This result gives a positive answer to a problem raised by E. I. Khukhro (see also Problem 14.96 from the Kourovka Notebook'' (1999, E. I. Khukhro and V. D. Mazurov (Eds.), The Kourovka Notebook: Unsolved Problems in Group Theory,'' 14th ed., Novosibirsk)).

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