Abstract
A semigroup S is an order in a semigroup Q if every element of Q is of the form q = a −1 b = cd −1 for some \({a,b,c,d\in S}\), where a −1 and d −1 are inverses within group \({{\mathcal H}}\) -classes of Q. We study orders in normal cryptogroups based on considering the restrictions of Green’s relations of Q to S. This produces certain relations which help us to gain an overview of all normal cryptogroups Q in which S is an order. Distinguished orders play an important role in this context.
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Petrich, M. On Orders in Normal Cryptogroups. Results. Math. 61, 75–96 (2012). https://doi.org/10.1007/s00025-010-0077-6
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DOI: https://doi.org/10.1007/s00025-010-0077-6