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621:"The Schützenberger Group of an H-class in the Semigroup of Binary Relations by Robert L. Brandon, Darel W. Hardy, George Markowsky, Missouri University of Science and Technology, 1972-12-01"
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Marcel-Paul Schützenberger (1957). "D-representation des demi-groupes".
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if and only if all of its Schützenberger groups are residually finite.
154:. In fact, there are two Schützenberger groups associated with a given
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Brandon, Robert; Hardy, Darel; Markowsky, George (December 1972).
514:, and it is naturally isomorphic to its own Schützenberger group.
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of mappings (taking functions as right operators). The group Γ(
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It is known that a monoid with finitely many left and right
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are distinct, but the groups associated with two different
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108:. The Schützenberger groups associated with different
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itself were a group, the Schützenberger group of the
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may be too technical for most readers to understand
442:) is the Schützenberger group associated with the
681:. Mathematical Surveys, No. 7. Providence, R.I.:
717:"Marcel-Paul Schützenberger (1920–1996)"
715:Wilf, Herbert; et al. (August 29, 1996).
525:and its Schützenberger group coincide for any
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426:. The set of all these transformations of
168:The Schützenberger group was discovered by
679:The algebraic theory of semigroups. Vol. I
192:be the semigroup obtained by adjoining an
172:in 1957 and the terminology was coined by
70:Learn how and when to remove this message
54:, without removing the technical details.
400:) defines a transformation, denoted by γ
721:The Electronic Journal of Combinatorics
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204:already has an identity element, then
591:all of its Schützenberger groups are
52:make it understandable to non-experts
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599:). Similarly such a monoid is
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683:American Mathematical Society
517:In general, one has that the
372:) be the set of all elements
671:Clifford, Alfred Hoblitzelle
499:is a maximal subgroup of a
147:would be isomorphic to the
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223:is defined as follows: If
170:Marcel-Paul Schützenberger
180:The Schützenberger group
675:Preston, Gordon Bamford
188:be a semigroup and let
705:(pp. 63–66)
652:C. R. Acad. Sci. Paris
122:contained in the same
434:), is a group under
88:Schützenberger group
18:Schutzenberger group
133:. Moreover, if the
129:of a semigroup are
637:10.1007/BF02572873
597:finitely generated
593:finitely presented
585:finitely generated
581:finitely presented
555:. You can help by
475:. You can help by
161:, with each being
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658:: 1994–1996.
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519:cardinality
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410:by mapping
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738:2015-12-30
607:References
380:such that
312:such that
268:such that
131:isomorphic
583:(or just
564:June 2009
484:June 2009
217:-relation
106:semigroup
752:Category
677:(1961).
456:Examples
120:-classes
113:-classes
701:0132791
527:H-class
512:H-class
506:, then
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