International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 263-266
doi:10.1155/S016117128900030X
A generalized Frattini subgroup of a finite group
Prabir Bhattacharya1
and N.P. Mukherjee2
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
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.