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Idempotents, regular elements and sequences from finite semigroups

✍ Scribed by T.E. Hall; M.V. Sapir

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
483 KB
Volume
161
Category
Article
ISSN
0012-365X

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✦ Synopsis

If n is the number of nonidempotent elements of a finite semigroup S, it is shown that each sequence of length 2 n of elements of S contains a consecutive subsequence whose product is an idempotent element, and that 2 n is the best possible among all finite semigroups with n nonidempotent elements. The proof remains valid if 'idempotent' is replaced by each of the words or phrases 'regular', 'group', 'core', 'regular and core' and 'group and core'. The best bound, among all semigroups S with ISI = n, is also found, for semigroups and for monoids with or without a zero.

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