JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 27-31.doi: 10.6040/j.issn.1671-9352.0.2024.130

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On the rank of the semigroup POm(n)

GOU Changsheng, RUAN Limin, ZHAO Ping*   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2025-11-11

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Abstract: Let Pn be a partial transformation semigroup on the finite set Xn={1,2,…,n}. Let 1≤m≤n, a subsemigroup of Pn be defined byPOm(n)={α∈Pn:Xm⊆dom(α), α|Xm∈Om},In the paper, the rank of the subsemigroup POm(n)is studied, where 1≤m≤n-1. For n≥3, it is proven thatrank POm(n)={2+2m, n-m=1,3+2m, n-m=2,4+2m, n-m≥3.

Key words: partial transformation semigroup, order-preserving full transformation semigroup, rank, generating set

CLC Number: 

  • O152.7
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