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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On Lagrangian groups

Authors: J. F. Humphreys and D. L. Johnson
Journal: Trans. Amer. Math. Soc. 180 (1973), 291-300
MSC: Primary 20D99
MathSciNet review: 0318312
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Abstract: We study the class $ \mathcal{L}$ of Lagrangian groups, that is, of finite groups $ G$ possessing a subgroup of index $ n$ for each factor $ n$ of $ \vert G\vert$. These groups and their analogues were considered by McLain in [4] and the object of the present work is to extend the results in this article. We study the classes $ (G) = \{ H\vert G \times H \in \mathcal{L}\} $ and also the closure of $ \mathcal{L}$ under wreath products. We also consider the two classes $ \mathfrak{X}$ and $ \mathfrak{Y}$ introduced in [2] and [4] respectively.

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Keywords: Supersoluble group, wreath product, KG-module, meet-irreducible, subgroup closure
Article copyright: © Copyright 1973 American Mathematical Society