Rendiconti del Seminario Matematico della Università di Padova

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Volume 129, 2013, pp. 17–33
DOI: 10.4171/RSMUP/129-2

Published online: 2013-05-15

Perfect numbers and finite groups

Tom De Medts[1] and Attila Maróti[2]

(1) Ghent University, Belgium
(2) 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.

Keywords: Perfect number, finite group

De Medts Tom, Maróti Attila: Perfect numbers and finite groups. Rend. Sem. Mat. Univ. Padova 129 (2013), 17-33. doi: 10.4171/RSMUP/129-2