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Butzman, S., Cannon, G., Paz, M.. (1401). Centers of centralizer nearrings determined by All endomorphisms of symmetric groups. فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), 13-26. doi: 10.22124/jart.2022.21398.1357
S. Butzman; G. A. Cannon; M. A Paz. "Centers of centralizer nearrings determined by All endomorphisms of symmetric groups". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 2, 1401, 13-26. doi: 10.22124/jart.2022.21398.1357
Butzman, S., Cannon, G., Paz, M.. (1401). 'Centers of centralizer nearrings determined by All endomorphisms of symmetric groups', فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), pp. 13-26. doi: 10.22124/jart.2022.21398.1357
Butzman, S., Cannon, G., Paz, M.. Centers of centralizer nearrings determined by All endomorphisms of symmetric groups. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 10(2): 13-26. doi: 10.22124/jart.2022.21398.1357

Centers of centralizer nearrings determined by All endomorphisms of symmetric groups

Journal of Algebra and Related Topics
دوره 10، شماره 2، اسفند 2022، صفحه 13-26    اصل مقاله (312.02 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2022.21398.1357
نویسندگان
S. Butzman1؛ G. A. Cannon* 2؛ M. A Paz1
1Department of Mathematics, Southeastern Louisiana University, Hammond, United States
2Department of Mathematics Southeastern Louisiana University Hammond, United States
چکیده
For $n = 5, 6$ and $E = \End S_n$, the functions in the centralizer nearring $M_E(S_n) = \{f : S_n \to S_n \ |\ f(1) = (1) \ \hbox{and} \ f \circ s = s \circ f \ \hbox{for all}\ s \in E\}$ are determined.  The centers of these two nearrings are also described.  Results that can be used to determine the functions in $M_E(S_n)$ and their centers for $n \geq 7$ are also presented.
 
کلیدواژه‌ها
centralizer nearring؛ symmetric group؛ center؛ outer automorphism
مراجع
  1. M. Boudreaux, G. A. Cannon, K. Neuerburg, T. Palmer, and T. Troxclair, Centers of centralizer nearrings determined by inner automorphisms of symmetric groups, J. Alg. Relat. Topics (1) 8 (2020), 51-65.
  2.  G. A. Cannon, Centralizer near-rings determined by End G, in Near-rings and near- elds (Fredericton, NB, 1993), Math. Appl., 336, Kluwer Acad. Publ., Dordrecht, 1995, 89-111.
  3.  G. A. Cannon, M. Farag, and L. Kabza, Centers and generalized centers of near-rings, Comm. Algebra (2) 35 (2007), 443- 453.
  4.  J. R. Clay, Nearrings: Geneses and Applications, Oxford University Press, Oxford, 1992.
  5.  G. Janusz and J. Rotman, Outer automorphisms of S6, Amer. Math. Monthly (6) 89 (1982), 407-410.
  6.  J. D. P. Meldrum, Near-Rings and Their Links with Groups, Research Notes in Math., No. 134, Pitman Publ. Co., London, 1985.
  7.  G. Pilz, Near-Rings, North-Holland/American Elsevier, Amsterdam, 1983.
  8.  M. Suzuki, Group Theory I, Springer-Verlag, 1982.
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