Minimal Presentations and Efficiency of Semigroups |
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Authors: | H Ayik C M Campbell J J O'Connor N Ruskuc |
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Institution: | H. Ayik*, C. M. Campbell, J. J. O'Connor, N. Ruskuc |
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Abstract: | A finite semigroup S is said to be efficient if it can be defined by a presentation (A | R) with |R| -|A|=rank(H2(S)). In this paper we demonstrate certain infinite classes of both efficient and inefficient semigroups. Thus, finite abelian groups, dihedral groups D2n 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. |
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