- Mathematical Sciences and Applications E-Notes
- Vol: 8 Issue: 1
- Some Properties on Sums of Element Orders in Finite p-groups
Some Properties on Sums of Element Orders in Finite p-groups
Authors : Nil MANSUROĞLU
Pages : 51-54
Doi:10.36753/mathenot.616086
View : 6 | Download : 4
Publication Date : 2020-03-20
Article Type : Research
Abstract :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 ( G ) denote the sum of element orders of a finite group G . As an immediate consequence, we proved that \psi( G ) ≤ 3 /4 \psi ( C ) and \psi( G ) < 1/ p - 1\psi ( C ), where G is a non-cyclic finite p -group of order p^ r and C is a cyclic group of order p^ r for some prime p .Keywords : finite p-group, group element order, , sum of element orders