Open AccessPerfect numbers and finite groups
Author(s) -
Tom De Medts,
Attila Maróti
Publication year - 2013
Publication title -
rendiconti del seminario matematico della università di padova
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 24
eISSN - 0373-319X
pISSN - 0041-8994
DOI - 10.4171/rsmup/129-2
Subject(s) - group (periodic table) , finite group , mathematics , order (exchange) , combinatorics , discrete mathematics , pure mathematics , physics , finance , quantum mechanics , economics
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
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