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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
##### Software:
MathOverflow; SageMath
Full Text:
##### References:
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