On Finite Generation and Presentability of Schützenberger Products
نویسنده
چکیده
The finite generation and presentation of Schützenberger products of semigroups are investigated. A general necessary and sufficient condition is established for finite generation. The Schützenberger product of two groups is finitely presented as an inverse semigroup if and only if the groups are finitely presented, but is not finitely presented as a semigroup unless both groups are finite. 2000 Mathematics subject classification: primary 20M05; secondary 20M18.
منابع مشابه
Finite Generation and Presentability of Wreath Products of Monoids
This paper gives necessary and sufficient conditions for the restricted wreath product of two monoids to be finitely generated or finitely presented.
متن کاملFor a few elements more: A survey of finite Rees index
This paper makes a comprehensive survey of results relating to finite Rees index for semigroups. In particular, we survey of the state of knowledge on whether various finiteness properties (such as finite generation, finite presentability, automaticity, and hopficity) are inherited by finite Rees index subsemigroups and extensions. We survey other properties that are invariant under passing to ...
متن کاملGroups Not Presentable by Products
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and certain geometric and measure or orbit equivalence invariants of groups on the other. This leads to many new examples of groups not presentable by products, incl...
متن کاملGroups Not Presentable by Products
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and certain geometric and measure or orbit equivalence invariants of groups on the other. This leads to many new examples of groups not presentable by products, incl...
متن کاملOn the Finite Presentation of Subdirect Products and the Nature of Residually Free Groups
We establish virtual surjection to pairs (VSP) as a general criterion for the finite presentability of subdirect products of groups: if Γ1, . . . ,Γn are finitely presented and S < Γ1×· · ·×Γn projects to a subgroup of finite index in each Γi × Γj , then S is finitely presentable, indeed there is an algorithm that will construct a finite presentation for S. We use the VSP criterion to character...
متن کامل