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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 263-266
http://dx.doi.org/10.1155/S016117128900030X

A generalized Frattini subgroup of a finite group

1Department of Computer Science, University of Nebraska - Lincoln, Lincoln 68588-0115, NE, USA
2School of Computer and System Sciences, Jawaharlal Nehru University, New Delhi 110067, India

Received 1 December 1987

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G). In particular, we obtain a characterization of G when each M in the definition of SP(G) is nilpotent.