Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On normal complements of $ \mathfrak{F}$-covering subgroups


Author: H. J. Schmidt
Journal: Proc. Amer. Math. Soc. 25 (1970), 457-459
MSC: Primary 20.40
MathSciNet review: 0258960
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ \mathcal{F}$ is a suitably restricted formation, we show that an $ \mathcal{F}$-covering subgroup $ H$ which is a Hall subgroup of the finite, solvable group $ G$ is complemented by the $ \mathcal{F}$-residual of $ G$, provided $ H$ normalizes an $ \mathcal{F}$-normalizer of $ G$. In particular, $ H$ is complemented by the $ \mathcal{F}$-residual, if $ H$ is an $ \mathcal{F}$-normalizer of $ G$. Further, if $ \mathcal{F}$ is the class of nilpotent groups, then $ H$ complements the nilpotent residual, if $ G$ has pronormal system normalizers. Examples are given to show the necessity of the various hypotheses.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20.40

Retrieve articles in all journals with MSC: 20.40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0258960-9
Keywords: Formation, solvable group, $ \mathcal{F}$-covering subgroup, $ \mathcal{F}$-normalizer, $ \mathcal{F}$-residual, Carter subgroup, Hall subgroup, pronormal subgroup, system normalizer
Article copyright: © Copyright 1970 American Mathematical Society