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      Homological finiteness properties of monoids, their ideals and maximal subgroups

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          Abstract

          We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is inherited by the maximal subgroups in a completely simple minimal ideal, in the case that the minimal ideal has finitely many left ideals. For completely simple semigroups we prove the converse, and as a corollary show that a completely simple semigroup is of type left- and right-FPn if and only if it has finitely many left and right ideals and all of its maximal subgroups are of type FPn. Also, given an ideal of a monoid, we show that if the ideal has a two-sided identity element then the containing monoid is of type left-FPn if and only if the ideal is of type left-FPn.

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          Most cited references 27

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          Morse theory and finiteness properties of groups

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            On the homology of associative algebras

             David Anick (1986)
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              Finiteness properties of arithmetic groups over function fields

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                Author and article information

                Journal
                16 March 2010
                Article
                1003.3227

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                20M50; 20J05
                25 pages
                math.GR

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