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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Huppert’s condition $B$
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by J. C. Beidleman PDF
Proc. Amer. Math. Soc. 43 (1974), 18-20 Request permission

Abstract:

Let $\mathcal {F}$ be a saturated formation of finite soluble groups. $\mathcal {F}$ is said to satisfy condition $\text {B}$ 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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • 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