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Proceedings of the American Mathematical Society

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

 

 

On Huppert's condition $ B$


Author: J. C. Beidleman
Journal: Proc. Amer. Math. Soc. 43 (1974), 18-20
MSC: Primary 20D10
DOI: https://doi.org/10.1090/S0002-9939-1974-0330281-9
MathSciNet review: 0330281
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Abstract: Let $ \mathcal{F}$ be a saturated formation of finite soluble groups. $ \mathcal{F}$ is said to satisfy condition B$ $ if and only if (a) $ \mathcal{F}$ is subgroup-closed, and (b) $ G \in \mathcal{F}$ and $ N$ a minimal normal subgroup of $ G$ implies $ \operatorname{Aut} (N) \in \mathfrak{F}$. The purpose of this note is to characterize those saturated formations of finite soluble groups which satisfy condition $ {\mathbf{B}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0330281-9
Keywords: Saturated formation, $ p$-rank, nilpotent, soluble
Article copyright: © Copyright 1974 American Mathematical Society