Year 2020, Volume 8 , Issue 1, Pages 51 - 54 2020-03-20

Some Properties on Sums of Element Orders in Finite p-groups

Nil MANSUROĞLU [1]


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.
finite p-group, group element order;, sum of element orders
  • [1] H. Amiri, S.M. Jafarian Amiri and I.M. Isaacs, Sums of element ordersin finite groups, Comm. Algebra. Volume 37, 2978-2980, 2009.
  • [2] H. Amiri, S.M. Jafarian Amiri, Sum of element orders on finite groupsof the same order, J. Algebra Appl., 10 (2), 187-190, 2011.
  • [3] S.M. Jafarian Amiri, Second maximum sum of element orders on finitenilpotent groups, Comm. Algebra, 41 (6), 2055-2059, 2013.
  • [4] H. Amiri, S.M. Jafarian Amiri, Second maximum sum of element orderson finite groups, J. Pure Appl. Algebra, 218 (3), 531-539, 2014.
  • [5] M. Herzog, P. Longobardi and M. Maj, An exact upper bound for sumsof element orders in non-cyclic finite groups, J. Pure and Applied Algebra, 222 (7), 1628{1642, 2018.
  • [6] E.I. Khukhro, p-Automorphisms of Finite p-Groups, London Mathematical Society Lecture Note Series 246, Cambridge University Press,1997.
  • [7] N. Mansuro˘glu, Sums of element orders in symmetric groups, AfyonKocatepe University Journal of Science and Engineering, 18, 884-887,2018.
  • [8] I.I. Martin, Finite group theory, Graduate Studies in Mathematics, 92,American Mathematical Society, Providence, RI, 2008.
  • [9] D. J. S. Robinson, A Course in the Theory of Groups, 2nd edition,Springer-Verlag, New York, 1996.
  • [10] R. Shen, G. Chen and C. Wu, On groups with the Second Largest Valueof the Sum of Element Orders, Comm. Algebra, 43 (6), 2618-2631, 2015.
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-6400-2115
Author: Nil MANSUROĞLU
Country: Turkey


Dates

Publication Date : March 20, 2020

Bibtex @research article { mathenot616086, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {51 - 54}, doi = {10.36753/mathenot.616086}, title = {Some Properties on Sums of Element Orders in Finite p-groups}, key = {cite}, author = {Mansuroğlu, Nil} }
APA Mansuroğlu, N . (2020). Some Properties on Sums of Element Orders in Finite p-groups . Mathematical Sciences and Applications E-Notes , 8 (1) , 51-54 . DOI: 10.36753/mathenot.616086
MLA Mansuroğlu, N . "Some Properties on Sums of Element Orders in Finite p-groups" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 51-54 <https://dergipark.org.tr/en/pub/mathenot/issue/53229/616086>
Chicago Mansuroğlu, N . "Some Properties on Sums of Element Orders in Finite p-groups". Mathematical Sciences and Applications E-Notes 8 (2020 ): 51-54
RIS TY - JOUR T1 - Some Properties on Sums of Element Orders in Finite p-groups AU - Nil Mansuroğlu Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.616086 DO - 10.36753/mathenot.616086 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 51 EP - 54 VL - 8 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.616086 UR - https://doi.org/10.36753/mathenot.616086 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes Some Properties on Sums of Element Orders in Finite p-groups %A Nil Mansuroğlu %T Some Properties on Sums of Element Orders in Finite p-groups %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 1 %R doi: 10.36753/mathenot.616086 %U 10.36753/mathenot.616086
ISNAD Mansuroğlu, Nil . "Some Properties on Sums of Element Orders in Finite p-groups". Mathematical Sciences and Applications E-Notes 8 / 1 (March 2020): 51-54 . https://doi.org/10.36753/mathenot.616086
AMA Mansuroğlu N . Some Properties on Sums of Element Orders in Finite p-groups. Math. Sci. Appl. E-Notes. 2020; 8(1): 51-54.
Vancouver Mansuroğlu N . Some Properties on Sums of Element Orders in Finite p-groups. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 51-54.
IEEE N. Mansuroğlu , "Some Properties on Sums of Element Orders in Finite p-groups", Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, pp. 51-54, Mar. 2020, doi:10.36753/mathenot.616086