On Residual Finiteness of Monoids, their Schutzenberger Groups and Associated Actions

Details On Residual Finiteness of Monoids, their Schutzenberger Groups and Associated Actions On Residual Finiteness of Monoids, their Schutzenberger Groups and Associated Actions

2010-03-16

arxiv.org/abs/1003.3176v1

Mathematics

Group Theory

20 pages, 3 figures

Scientific paper

In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M; (RFSG) residual finiteness of Schutzenberger groups of M; and (RFRL) residual finiteness of the natural actions of M on its Green's R- and L-classes. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We consider these questions in all the possible combinations of the following situations: M is an arbitrary monoid; M is an arbitrary regular monoid; every J-class of M has finitely many R- and L-classes; M has finitely many left and right ideals. In each case we obtain complete answers.

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