An exact upper bound for sums of element orders in non-cyclic finite groups

2016/10/12 by Herzog, Marcel, Longobardi, Patrizia, Maj, Mercede
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1610.03669

Abstract

Denote the sum of element orders in a finite group G by ψ(G) and let C_n denote the cyclic group of order n. Suppose that G is a non-cyclic finite group of order n and q is the least prime divisor of n. We proved that ψ(G)≤\frac 711ψ(C_n) and ψ(G)

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