On products of all elements of a finite semigroup

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Let S be a finite semigroup. Consider the set p(S) of all elements of S which can be represented as a product of all the elements of S in some order. It is shown that p(S) is contained in the minimal ideal M of S and intersects each maximal subgroup H of M in essentially the same way. The main result shows that p(S) intersects H in a union of cosets of H'.

Original languageEnglish
Pages (from-to)551-557
Number of pages7
JournalProceedings of the Edinburgh Mathematical Society
Issue number3
Publication statusPublished - Oct 1999


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