JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 6-10.doi: 10.6040/j.issn.1671-9352.0.2023.545

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Rank of the 2-singular transformation semigroup Tn(2)

GAO Ronghai1, XU Bo2   

  1. 1. Journal Editorial Department, Guizhou Normal University, Guiyang 550025, Guizhou, China;
    2. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2025-11-11

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Abstract: Let n≥4, Xn={1,2,…,n}. Singn is singular transformation semigroup on Xn. for α∈Singn, α is called 2-singular transformation if it exists x∈Xn\{1} that satisfy xα=1α or exists x∈Xn\{2} that satisfy xα=2α. Let Tn(2) be consisting of all 2-singular transformations in Singn. A minimum generating set is determined through the construction method, and it is proved that the rank of Tn(2) is 2n-3.

Key words: 2-singular transformation, semigroup, generation set, rank

CLC Number: 

  • O152.7
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