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Mat. Zametki, 1976, Volume 19, Issue 3, Pages 401–418 (Mi mz7759)  

Groups of automorphisms of finite $p$-groups

A. V. Borovik, E. I. Khukhro

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR

Abstract: Thompson [1] showed that if $p$ is an odd prime number, $A$ is a $p$-group of operators of the finite group $P$ in which the Frattini subgroup $\Phi(P)$ is elementary and central, and $P/\Phi(P)$ is a free $Z_pA$-module, then $C_P(A)$ covers $C_{P/\Phi(P)}(A)$. Then he proposed the question of whether it is possible in this theorem to weaken the hypothesis that $\Phi(P)$ be elementary and central. In the work it is shown that this hypothesis may be replaced by a much weaker one; it is sufficient that P be met-Abelian and have nilpotence class prime-subgroups of Sylowizers of a $p$-subgroup of a solvable group [2].

Full text: PDF file (1237 kB)

English version:
Mathematical Notes, 1976, 19:3, 245–255

Bibliographic databases:

UDC: 519.44
Received: 12.08.1975

Citation: A. V. Borovik, E. I. Khukhro, “Groups of automorphisms of finite $p$-groups”, Mat. Zametki, 19:3 (1976), 401–418; Math. Notes, 19:3 (1976), 245–255

Citation in format AMSBIB
\Bibitem{BorKhu76}
\by A.~V.~Borovik, E.~I.~Khukhro
\paper Groups of automorphisms of finite $p$-groups
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 3
\pages 401--418
\mathnet{http://mi.mathnet.ru/mz7759}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=414703}
\zmath{https://zbmath.org/?q=an:0361.20033|0347.20011}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 3
\pages 245--255
\crossref{https://doi.org/10.1007/BF01437859}


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