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On products of all elements of a finite semigroup

Published online by Cambridge University Press:  20 January 2009

P. Z. Hermann ,
E. F. Robertson  and
N. Ruškuc
P. Z. Hermann
Affiliation:
Department of Algebra and Number Theory, Eötvös Loránd University, Múzeum Krt. 6–8, Budapest, H-1088 Hungary, E-mail address: hp@cs.elte.hu
E. F. Robertson
Affiliation:
Department of Algebra and Number Theory, Eötvös Loránd University, Múzeum Krt. 6–8, Budapest, H-1088 Hungary, E-mail address: hp@cs.elte.hu
N. Ruškuc
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland, E-mail addresses: efr@st-and.ac.uk, nr1@st-and.ac.uk
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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′.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 3 , October 1999 , pp. 551 - 557
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

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