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Minimal Presentations and Efficiency of Semigroups (2000)

Ayik*, H. ; Campbell, C. M. ; O'Connor, J. J. ; [et al.]

Springer

Semigroup forum 60 (2000), S. 231-242

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ISSN: 1432-2137

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: S is said to be efficient if it can be defined by a presentation (A | R) with |R| -|A|=rank(H 2(S)). In this paper we demonstrate certain infinite classes of both efficient and inefficient semigroups. Thus, finite abelian groups, dihedral groups D 2 n with n even, and finite rectangular bands are efficient semigroups. By way of contrast we show that finite zero semigroups and free semilattices are never efficient. These results are compared with some well-known results on the efficiency of groups.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002339910016

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