In this paper, we show that CLn, the chain with n elements, is efficient and that the direct product CLm × CLn is inefficient. Moreover, we embed any finitely presented semigroup S into an inefficient semigroup, namely, the semigroup S ⋃ SLn, where SLn is the free semilattice of rank n.
A new efficient presentation for P SL (2,5) In this paper, we study the structure of G(3, m, n). We also give a new efficient presentation for the Projective Special Linear group P SL(2, 5) and in particular we prove that P SL(2, 5) is isomorphic to G(3, m, n) under certain conditions.
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