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Abstract
The diagonal right (respectively, left) act of a semigroup S is the set S x S on which S acts via (x, y)s = (xs, ys) (respectively, s(x, y) = (sx, sy)), the same set with both actions is the diagonal biact. The diagonal right (respectively, left, bi) act is said to be finitely generated if there is a finite set A subset of S x S such that S x S = AS' (respectively, S x S = S(1)A, S x S = S(1)AS(1)).
In this paper we consider the question of finite generation for diagonal acts of certain infinite semigroups of transformations and relations. We show that the semigroups of full transformations, partial transformations and binary relations on an infinite set each have cyclic diagonal right and left acts. The semigroup of full finitetoone transformations on an infinite set has a cyclic diagonal right act but its diagonal left act is not finitely generated. The semigroup of partial injections on an infinite set has neither finitely generated diagonal right nor left act, but has a cyclic diagonal biact. The semigroup of bijections (symmetric group) on an infinite set does not have any finitely generated diagonal acts.
Original language  English 

Pages (fromto)  139146 
Number of pages  8 
Journal  Bulletin of the Australian Mathematical Society 
Volume  72 
DOIs  
Publication status  Published  Aug 2005 
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Dive into the research topics of 'Finite generation of diagonal acts of some infinite semigroups of transformations and relations'. Together they form a unique fingerprint.Projects
 1 Finished

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications
Linton, S. A., Gent, I. P., Leonhardt, U., Mackenzie, A., Miguel, I. J., Quick, M. & Ruskuc, N.
1/09/05 → 31/08/10
Project: Standard