Sequences with idempotent products from finite regular semigroups |
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Authors: | Jean Oesmer Loyola |
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Institution: | Institute of Mathematical Sciences and Physics, CAS, University of Philippines Los Baños, College Laguna, Philippines 4031 |
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Abstract: | We find the smallest integer (n) such that for every regular semigroup S of order n, every sequence of length (n) of elements of S contains a consecutive subsequence whose product is an -element, where = ‘idempotent’, ‘core’ and ‘subgroup and core’. For arbitrary semigroups of order n, we also find (n) where = ‘regular’, ‘group’, ‘core’, ‘regular and core’ and ‘subgroup and core’. |
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