Congruences associated with families of nilpotent subgroups and a theorem of Hirsch

Abstract

Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order.

Keywords

• Nilpotent systems of subgroups
• congruences