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

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

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 ofelement orders in finite p-groups and to give some properties of such sums. Let ψ(G) denote the sum ofelement orders of a finite group G. As an immediate consequence, we proved that ψ(G)

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