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 Φ(P) is elementary and central, and P/Φ(P) is a free ZpA-module, then Cp(A) covers CP/Φ(P)(A). Then he proposed the question of whether it is possible in this theorem to weaken the hypothesis that Φ(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 <p. From examples it is seen that the restriction on the nilpotence class of P is essential. As a corollary we obtain the negative solution for all prime numbers p of Gaschutz's problem concerning the conjugacy of Hall p′-subgroups of Sylowizers of a p-subgroup of a solvable group [2].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Mathematical Notes of the Academy of Sciences of the USSR
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
