A number is perfect if it is the sum of its proper divisors. We extend this notion to finite groups by calling a finite group a Leinster group if its order is equal to the sum of the orders of all proper normal subgroups of the group. We provide some general theory, we present examples of Leinster groups, and we prove some related results.
Cite this article
Tom De Medts, Attila Maróti, Perfect numbers and finite groups. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 17–33DOI 10.4171/RSMUP/129-2