- Mathematical Sciences and Applications E-Notes
- Volume: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 : 52 | Download : 24
Publication Date : 2020-03-20
Article Type : Research Paper
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 insert ignore into journalissuearticles values( G ); denote the sum of element orders of a finite group G . As an immediate consequence, we proved that \psiinsert ignore into journalissuearticles values( G ); ≤ 3 /4 \psi insert ignore into journalissuearticles values( C ); and \psiinsert ignore into journalissuearticles values( G ); < 1/ p - 1\psi insert ignore into journalissuearticles values( 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
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