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1. Algebra and Number Theory

An average equal to 1 for every non-trivial finite group

Mihai Chiş
West University of Timişoara, Timişoara, Romania

Abstract:

For a finite group $G$ and and a set $T^*$ of representatives for the conjugacy classes of non-trivial elements of $G$, we define a canonical integer associated with every element in $T^*$ and show that the average value of this over $T^*$ is equal to $1$.