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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 55-62.doi: 10.6040/j.issn.1671-9352.0.2019.636

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有限弱Y-稳定变换半群的极大子半群

金久林1,腾文1,2,祝富洋1,游泰杰1*,瞿云云1   

  1. 1.贵州师范大学数学科学学院, 贵州 贵阳 550001;2.贵州财经大学数学与统计学院, 贵州 贵阳 550025
  • 出版日期:2020-10-20 发布日期:2020-10-07
  • 作者简介:金久林(1991— ), 男, 博士研究生, 研究方向为信息代数、半群代数及其应用. E-mail:JinJiuLin2016@163.com*通信作者简介:游泰杰(1959— ), 男, 硕士, 教授, 博士生导师, 研究方向为信息代数、半群代数及其应用. E-mail:youtaijie1111@163.com
  • 基金资助:
    贵州省一流建设学科计划资助项目(C420001);贵州省科学技术基金资助项目(黔科合基础［2019］1221号)

Maximal subsemigroups of the finite transformation semigroup of weak Y-stabilizer

JIN Jiu-lin1, TENG Wen1,2, ZHU Fu-yang1, YOU Tai-jie1*, QU Yun-yun1   

  1. 1. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China;
    2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China
  • Online:2020-10-20 Published:2020-10-07

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摘要： 设X是一个非空集合,T(X)是X上的全变换半群。对X的任意非空子集Y,令T(X,Y)={α∈T〓(X):Yα⊆Y},称其为弱Y-稳定变换半群。当X为有限集且Y是X的非单点真子集时,给出了T(X,Y)的极大子半群的结构与完全分类。

关键词: 变换半群, 弱Y-稳定, 极大子半群

Abstract: Let X be a non-empty set. Denote by T (X)the full transformation semigroup on X. Given a non-empty subset Y of X, letT(X,Y)={α∈T (X):Yα⊆Y}, and call it the transformation semigroup of weak Y-stabilizer. In this paper, we show that structure and complete classification of maximal subsemigroups of T(X,Y)whenever Y is a proper non-singleton subset of finite set X.

Key words: transformation semigroup, weak Y-stabilizer, maximal subsemigroup

中图分类号: 

  • O152.7
[1] DÉNES J. On transformations, transformation semigroups and graphs[J]. Theory of Graphs Proc Colloq Tihany, 1966: 65-75.
[2] BAĬRAMOV R A. On the problem of completeness in a symmetric semigroup of finite degree[J]. Diskret Analiz, 1966, 8:3-26.
[3] TODOROV K, KRACOLOVA L. On the maximal subsemigroups of the ideals of finite symmetric semigroup[J]. Simon Stevin, 1985, 59(2):129-140.
[4] YOU Taijie. Maximal regular subsemigroups of certain semigroups of transformations[J]. Semigroup Forum, 2002, 64(3):391-396.
[5] YANG Haobo, YANG Xiuliang. Maximal subsemigroups of finite transformation semigroups K(n,r)[J]. Acta Mathematica Sinica, 2004, 20(3):475-482.
[6] EAST J, MITCHELL J D, PÉRESSE Y. Maximal subsemigroups of the semigroup of all mappings on an infinite set[J]. Transactions of the American Mathematical Society, 2015, 367(3):1911-1944.
[7] CHAIYA Y, HONYAM P, SANWONG J. Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets[J]. Turkish Journal of Mathematics, 2017, 41(1):43-54.
[8] 高荣海. P On的极大幂等元生成子半群[J]. 贵州师范大学学报(自然科学版), 2012, 30(4):66-68. GAO Ronghai. Maximal idempotent-generated subsemigroups of P On[J]. Journal of Guizhou Normal University(Natural Sciences), 2012, 30(4):66-68.
[9] 金久林, 游泰杰, 孙艳, 等. 全变换半群的极大子左(右)群[J]. 贵州师范大学学报(自然科学版), 2016, 34(6):52-55. JIN Jiulin, YOU Taijie, SUN Yan, et al. Maximal left(right)group of the full transformation semigroup[J]. Journal of Guizhou Normal University(Natural Sciences), 2016, 34(6):52-55.
[10] 金久林, 游泰杰. 半群MC(n,r)的极大子半群[J]. 吉林大学学报(理学版), 2017, 55(3):523-530. JIN Jiulin, YOU Taijie. Maximal subsemigroups of semigroup MC(n,r)[J]. Journal of Jilin University(Science Edition), 2017, 55(3):523-530.
[11] 金久林, 游泰杰, 徐波. 有限全变换半群变种具有某种性质的极大子半群[J]. 吉林大学学报(理学版), 2018, 56(3):549-555. JIN Jiulin, YOU Taijie, XU Bo. Maximal subsemigroups of some properties in variants of finite full transformation semigroups[J]. Journal of Jilin University(Science Edition), 2018, 56(3):549-555.
[12] MAGILL K D. Subsemigroups of S(X)[J]. Math Japan, 1966, 11:109-115.
[13] YANG Xiuliang, YANG Haobo. Maximal half-transitive submonoids of full transformation semigroup[J]. Advances Mathematics, 2011, 40(5):580-586.
[14] HONYAM P, SANWONG J. Semigroups of transformations with invariant set[J]. Journal of the Korean Mathematical Society, 2011, 48(2):289-300.
[15] 冯正浩, 杨秀良. 有限弱Y-稳定变换半群的极小同余[J]. 浙江大学学报(理学版), 2011, 38(5):495-496. FENG Zhenghao, YANG Xiuliang. Minimal congruences on finite transformation semigroup of weak Y-stabilizer[J]. Journal of Zhejiang University(Science Edition), 2011, 38(5):495-496.
[16] 张佳. 变换半群的完全正则性和超富足性[J]. 西南大学学报(自然科学版), 2011, 33(8):99-101. ZHANG Jia. Complete regularity and super-abundance of some transformation semigroups[J]. Journal of Southwest University(Natural Science Edition), 2011, 33(8):99-101.
[17] 张佳. 一类变换半群的极大逆子半群[J]. 阜阳师范学院学报(自然科学版), 2016, 33(3):6-7,16. ZHANG Jia. A class of maximal inverse sub-semigroups of some transformation semigroups[J]. Journal of Fuyang Normal University(Natural Science), 2016, 33(3):6-7,16.
[18] 金久林, 祝富洋, 游泰杰, 等. 有限弱Y-稳定变换半群的秩[J]. 东北师大学报(自然科学版), 2020,52(3):50-55. JIN Jiulin, ZHU Fuyang, YOU Taijie, et al. Rank of the finite transformation semigroup of weak Y-stabilizer[J]. Journal of Northeast NormalUniversity(Natural Science Edition), 2020, 52(3):50-55.
[19] SUN Lei, WANG Limin. Natural partial order in semigroups of transformations with invariant set[J]. Bulletin of the Australian Mathematical Society, 2013, 87(1):94-107.
[20] SUN Lei, SUN Junling. A note on natural partial order in semigroups of transformations with invariant set[J]. Bulletin of the Australian Mathematical Society, 2015, 91(2):264-267.
[21] ZHANG Jia, LUO Yanfeng. On certain order-preserving transformation semigroups[J]. Communications in Algebra, 2017, 45(7):2980-2995.
[22] TOKER K, AYIK H. On the rank of transformation semigroup T(n,m)[J]. Turkish Journal of Mathematics, 2018, 42:1970-1977.
[23] CHINRAM R, BAUPRADIST S. Magnifying elements of semigroups of transformations with invariant set[J/OL]. Asian-European Journal of Mathematics, [2018-5-23]. https://doi.org/10.1142/S1793557119500566.
[24] HOWIE J M. Fundamentals of semigroup theory[M]. London: Oxford University Press, 1995.
[25] LIEBECK M W, PRAEGER C E, SAXL J. A classification of the maximal subgroups of the finite alternating and symmetric groups[J]. Journal of Algebra, 1987, 111:365-383.
[26] THÉVENAZ J. Maximal subgroups of direct products[J]. Journal of Algebra, 1997, 198:352-361.
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