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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2017, Issue 2(31), Pages 46–49
(Mi pfmt501)
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MATHEMATICS
A criterion for a finite group to belong a saturated formation
I. M. Dergacheva, I. P. Shabalina, E. A. Zadorozhnyuk Belarusian State University of Transport
Abstract:
We prove the following result: Let F be a hereditary saturated formation of p-soluble groups containing all p-supersoluble
groups such that F=GpF. Let G=AT where A is a Hall π-subgroup of G, p∉π and T is a p-supersoluble subgroup of G. Suppose that for a Sylow p-subgroup P of T we have |P|>p. If A permutes with a Hall p′-subgroup of T and with all
maximal subgroups V of P such that GF∩P⩽/V, then G∈F.
Keywords:
finite group, saturated formation, p-soluble group, p-supersoluble group, Hall subgroup.
Received: 29.04.2017
Citation:
I. M. Dergacheva, I. P. Shabalina, E. A. Zadorozhnyuk, “A criterion for a finite group to belong a saturated formation”, PFMT, 2017, no. 2(31), 46–49
Linking options:
https://www.mathnet.ru/eng/pfmt501 https://www.mathnet.ru/eng/pfmt/y2017/i2/p46
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Abstract page: | 215 | Full-text PDF : | 45 | References: | 46 |
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