Some properties on sums of element orders in finite p-groups

Nil MANSUROĞLU
2020 Mathematical sciences and applications e-notes  
In literature, there are many papers on the sum of element orders of a finite group. In this study, in particular, we deal with the cases in finite p-groups. Our main aim is to investigate the sums of element orders in finite p-groups and to give some properties of such sums. Let ψ(G) denote the sum of element orders of a finite group G. As an immediate consequence, we proved that ψ(G) < 3 4 ψ(C) and ψ(G) < 1 p−1 ψ(C), where G is a non-cyclic finite p-group of order p r and C is a cyclic group
more » ... is a cyclic group of order p r for some prime p.
doi:10.36753/mathenot.616086 fatcat:tbw4okjq6jhcxlngo5c74xivxm