Email this article Abnormality Criteria for p-Complements
- Authors: Vdovin E.P.1,2, Revin D.O.1,2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 55, No 5 (2016)
- Pages: 347-353
- Section: Article
- URL: https://journal-vniispk.ru/0002-5232/article/view/234001
- DOI: https://doi.org/10.1007/s10469-016-9406-5
- ID: 234001
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Abstract
It is proved that for any finite group G possessing a p-complement H for some prime number p, the following assertions are equivalent: (1) all p-complements of G are self-normalizable; (2) all p-complements of G are abnormal; (3) the subgroup H is abnormal in G; (4) NG(HX) = HX for any \( X\underline{\vartriangleleft}\;G \); (5) G does not contain central chief p-factors.
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About the authors
E. P. Vdovin
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: vdovin@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
D. O. Revin
Sobolev Institute of Mathematics; Novosibirsk State University
Email: vdovin@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
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