Volume no :71, Issue no: 1, November (2022)

Journal of Mathematical Sciences: Advances and Applications

A SIMPLE PROOF THAT MINIMAL NORMAL SUBGROUPS OF FINITE GROUPS ARE DIRECT PRODUCTS OF ISOMORPHIC SIMPLE GROUPS

Author's: Chrystopher L. Nehaniv
Pages: [1] - [4]
Received Date: August 26, 2022
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122262

Abstract

We give a short self-contained proof of the important classical result that a minimal normal subgroup of a finite group is an internal direct product of isomorphic simple groups (e.g., Theorem 8.6.1 of M. Hall’s The Theory of Groups, The MacMillan Co., 1966; Corollary 5.27 of J. J. Rotman’s An Introduction to the Theory of Groups, Springer Verlag, 1995; Theorem 4.3A (iii) of J. D. Dixon & B. Mortimer’s Permutation Groups, Springer Verlag, 1996).

Keywords

finite groups, minimal normal subgroups, structure theory, finite simple groups, tutorial exposition.