Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

  • [1] B. Huppert, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften, Band 134, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
  • [2] D. L. Johnson, A note on supersoluble groups, Canad. J. Math. 23 (1971), 562-564. MR 43 #7513. MR 0281799 (43:7513)
  • [3] D. J. McCarthy, A survey of partial converses to Langrange's theorem on finite groups, Trans. New York Acad. Sci. 33 (1971), 586-594. MR 0311766 (47:328)
  • [4] D. H. McLain, The existence of subgroups of given order in finite groups, Proc. Cambridge Philos. Soc. 53 (1957), 278-285. MR 19, 13. MR 0085260 (19:13e)
  • [5] O. Ore, Contributions to the theory of groups of finite order, Duke Math. J. 5 (1939), 431-460. MR 1546136
  • [6] G. Zappa, Remark on a recent paper of O. Ore, Duke Math. J. 6 (1940), 511-512. MR 2, 1. MR 0002118 (2:1f)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20D99

Retrieve articles in all journals with MSC: 20D99

Additional Information

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

American Mathematical Society