On certain semigroups of partial contractions of a finite chain

2018/03/07 by Umar, A., Zubairu, M. M.
#20M20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1803.02604

Abstract

Let [n]=\1,2,…,n\ be a finite chain and let P_n be the semigroup of partial transformations on [n]. Let CP_n=\α∈ P_n: (for ~all~x,y∈ Dom~α)~|xα-yα|≤|x-y|\ be the subsemigroup of partial contraction mappings on [n]. We have shown that the semigroup CP_n and some of its subsemigroups are nonregular left abundant semigroups for all n but not right abundant for n≥ 4.

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