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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
DOI: https://doi.org/10.1090/S0002-9947-1973-0318312-7
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 $|G|$. 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 $(G) = \{ H|G \times H \in \mathcal {L}\}$ 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, <I>KG</I>-module, meet-irreducible, subgroup closure
Article copyright: © Copyright 1973 American Mathematical Society