Sums of Element Orders in Symmetric Groups

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.

Synthesis, Characterization and Dielectric Behavior of (4- Diethanolaminomethyl Styrene-co-Benzylmethacrylate) Polymer and Its Co (II), Ni (II) and Zn (II)-Metal Complexes

In this study, 4-diethanolaminomethyl styrene (DEAMSt) and benzyl methacrylate (BMA) copolymer were synthesized. The synthesized copolymer was characterized by spectral techniques such as FT-IR, 1H-NMR, Elemental analysis, SEM, XRD, DSC and TGA. This copolymer obtained is used as ligand and its metal complexes were prepared with Co (II), Ni (II) and Zn (II) metal ions. The copolymer-metal complexes were characterized by the above spectral techniques. In addition, magnetic measurements of copolymer-metal complexes were received. The geometric structures of the copolymer-metal complexes according to magnetic measurements were estimated that have a tetrahedral geometric structure. The ligand was found an amorphous structure and metal complexes were found to be crystal structure by XRD analysis. The composition of the copolymer was determined by 1H-NMR spectra and the composition ofDEAMSt% was found as 23%. The average molecular weights and polydispersity index of the (DEAMSt0.23-ko-BMA) polymer were determined by gel permation choromatography. Glasstransition temperature and thermal behaviors determined by DSC and TGA. The dielectric properties of ligand and copolymer metal complexes were investigated as a function of frequency.

Keywords:

Copolymer-Metal, Ligand, Complexes, Dielectirical Properties, Copolymer, Magnetic, Measurements,

PDF

___

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.