Leinster group

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Definition

In words

A group is called a Leinster group if the sum of the orders of its proper normal subgroups is equal to its order.

In symbols

A group $G$ is called a Leinster group if $\sum _{N\trianglelefteq G,N\neq G}|N|=|G|$.

Examples

Let $N$ be a perfect number (a number whose proper divisors sum to itself). Then the cyclic group of order $N$ is a Leinster group.

There is a non-abelian Leinster group of order 355433039577. This is the smallest known non-abelian Leinster group of odd order.

The smallest Leinster groups (those of order 6, 12, 28) are cyclic group:Z6, dicyclic group:Dic3, cyclic group:Z28.

External links

A086792 in the OEIS, the orders of the Leinster groups, begins 6, 12, 28, 30, 56, 360, 364, 380, 496, 760, 792, 900, 992, 1224, 1656, 1680, 1980....