[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.
Some Properties on Sums of Element Orders in Finite p-groups
Year 2020,
Volume: 8 Issue: 1, 51 - 54, 20.03.2020
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.
[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.
Mansuroğlu, N. (2020). Some Properties on Sums of Element Orders in Finite p-groups. Mathematical Sciences and Applications E-Notes, 8(1), 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. March 2020;8(1):51-54. doi:10.36753/mathenot.616086
Chicago
Mansuroğlu, Nil. “Some Properties on Sums of Element Orders in Finite P-Groups”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 51-54. https://doi.org/10.36753/mathenot.616086.
EndNote
Mansuroğlu N (March 1, 2020) Some Properties on Sums of Element Orders in Finite p-groups. Mathematical Sciences and Applications E-Notes 8 1 51–54.
IEEE
N. Mansuroğlu, “Some Properties on Sums of Element Orders in Finite p-groups”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 51–54, 2020, doi: 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.
JAMA
Mansuroğlu N. Some Properties on Sums of Element Orders in Finite p-groups. Math. Sci. Appl. E-Notes. 2020;8:51–54.
MLA
Mansuroğlu, Nil. “Some Properties on Sums of Element Orders in Finite P-Groups”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 51-54, doi:10.36753/mathenot.616086.
Vancouver
Mansuroğlu N. Some Properties on Sums of Element Orders in Finite p-groups. Math. Sci. Appl. E-Notes. 2020;8(1):51-4.