International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 821-824
doi:10.1155/S0161171294001158
A note on p-solvable and solvable finite groups
1Mathematics Department, College of Science Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
2Department of Mathematics Jawaharlal Nehru University, New Delhi 110067, India
Received 19 January 1993
Copyright © 1994 R. Khazal and N. P. Mukherjee. 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
The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p-solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p-solvable and normal solvable subgroups, respectively, of G.