JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (12): 81-85.doi: 10.6040/j.issn.1671-9352.0.2022.126

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Rank of the 1-singular transformation semigroup Tn(1)

XU Bo1, GAO Rong-hai2, LU Lin-zhang1,3, YOU Tai-jie1   

  1. 1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, Guizhou, China;
    2. Editorial Department of Journal of Guizhou Normal University, Guizhou Normal University, Guiyang 550001, Guizhou, China;
    3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China
  • Published:2022-12-05

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Abstract: Let n≥4, and Xn={1,2,…,n}. A new class of subsemigroups, 1-singular transformation semigroups of total transformation semigroups, is defined by non-singleton property, denoted by Tn(1). After determining the minimum generating set of the 1-singular transformation semigroup Tn(1)on Xn by idempotent analysis, it is proved that the rank of Tn(1)is n.

Key words: 1-singular transformation, semigroup, rank

CLC Number: 

  • O152.7
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