Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On a theorem of Deskins

Author: Irene Zimmermann
Journal: Proc. Amer. Math. Soc. 107 (1989), 895-899
MSC: Primary 20D10; Secondary 20D30
MathSciNet review: 986654
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we present a solvability criterion for finite groups. We show that a finite group $ G$ is solvable if in every maximal subgroup chain of length 3 of $ G$ at least one term is a submodular subgroup of $ G$. This generalizes an earlier result of Deskins.

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

  • [1] M. Asaad, Generalization of a theorem of Deskins, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 18 (1975), 177-179. MR 0417287 (54:5344)
  • [2] W. E. Deskins, A condition for the solvability of a finite group, Illinois J. Math. 5 (1961), 306-313. MR 0124396 (23:A1708)
  • [3] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin-Heidelberg-New York, 1979. MR 0224703 (37:302)
  • [4] B. Huppert and N. Blackburn, Finite groups III, Springer-Verlag, Berlin-Heidelberg-New York 1982. MR 662826 (84i:20001b)
  • [5] R. Schmidt, Modulare Untergruppen endlicher Gruppen, Illinois J. Math. 13 (1969), 358-377. MR 0258972 (41:3617)
  • [6] I. Zimmermann, Submodular subgroups in finite groups, (to appear in Math. Z). MR 1022820 (90h:20028)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D10, 20D30

Retrieve articles in all journals with MSC: 20D10, 20D30

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society