Perfect numbers and finite groups

  • Tom De Medts

    Ghent University, Belgium
  • Attila Maróti

    Hungarian Academy, Budapest, Hungary


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. 17–33

DOI 10.4171/RSMUP/129-2