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Perfect numbers and finite groups. (English) Zbl 1280.20026
A number is said to be perfect if it is the sum of its proper divisors. In the current paper this notion is extended to finite groups by calling a finite group a Leinster group if its order is equal to the sum of the orders of all its proper normal subgroups. Several general results and examples of Leinster groups are presented.

MSC:
20D60 Arithmetic and combinatorial problems involving abstract finite groups
11A25 Arithmetic functions; related numbers; inversion formulas
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