Year: 2001
Type: preprint
Abstract: A number is perfect if it is the sum of its proper divisors; here we call a finite group `perfect' if its order is the sum of the orders of its proper normal subgroups. (This conflicts with standard terminology but confusion should not arise.) The notion of perfect group generalizes that of perfect number, since a cyclic group is perfect exactly when its order is perfect. We show that, in fact, the only abelian perfect groups are the cyclic ones, and exhibit some non-abelian perfect groups of even order.
Source: arXiv (Cornell University)
Author: Leinster, Tom
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1680408482