Sums of Element Orders in Symmetric Groups

Yıl 2018, Cilt: 18 Sayı: 3, 884 - 887, 30.12.2018

Nil Mansuroğlu

Öz

In literature, there are many papers on the sums of element orders of finite groups. In this study we deal with the cases in symmetric groups. Our main aim is to investigate the sums of element orders in symmetric groups and to give some properties of the sum of element orders in symmetric group. Moreover, we derive the formula for such sums.

Anahtar Kelimeler

Finite group, Symmetric groups, Sum of orders element, Element order.

Kaynakça

• Amiri, S.M., 2009. Sums of element orders in finite groups. Communication Algebra, 39, 2978-2980.
• Amiri, S.M. and Amiri, J., 2011. Sum of element orders on finite groups of same order. Journal of Algebra and Its Applications, 10, 2, 187-190.
• Gorenstein, D.,1968. Finite groups, Harper and Row, New York.
• Herstein, E.N., 1958. A remark on finite groups. Proceedings of the American Mathematical Society, 9, 2, 255-257.
• Herzog, M., Longobardi, P. and Maj, M., 2018. An exact upper bound for sums of element orders in non-cyclic finite groups. Journal of Pure and Applied Algebra, 222, 7, 1628- 1642.
• Robinson, D.J.S., 1996. A course in the theory of groups, Springer, New York, 516pp.