Title of article :
The minimum sum of element orders of finite groups
Author/Authors :
Jahani, Maghsoud Department of Mathematics - Shabestar Branch - Islamic Azad University , Marefat, Yadollah Department of Mathematics - Shabestar Branch - Islamic Azad University , Refaghat, Hasan Department of Mathematics - Tabriz Branch - Islamic Azad University , Vakili Fasaghandisi, Bahram Department of Mathematics - Shabestar Branch - Islamic Azad University
Abstract :
Let G be a finite group and ψ(G)=∑g∈Go(g), where o(g) denotes the order of g∈G. We show that the Conjecture 4.6.5 posed in [Group Theory and Computation, (2018) 59-90], is incorrect. In fact, we find a pair of finite groups G and S of the same order such that ψ(G)<ψ(S), with G solvable and S simple.
Keywords
Keywords :
Finite group , element orders sum , solvable group , simple group
Journal title :
International Journal of Group Theory
