Generic Representations of Finitely Generated Groups on Fraisse Structures

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

Finitely approximable groups and actions Part II: Generic representations

Given a finitely generated group Γ, we study the space Isom(Γ,QU) of all actions of Γ by isometries of the rational Urysohn metric space QU, where Isom(Γ,QU) is equipped with the topology it inherits seen as a closed subset of Isom(QU). When Γ is the free group Fn on n generators this space is just Isom(QU) , but is in general significantly more complicated. We prove that when Γ is finitely gen...

A characterization of finitely generated multiplication modules

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

On finitely generated modules whose first nonzero Fitting ideals are regular

A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...

Generic Subgroups of Group Amalgams

For many groups the structure of finitely generated subgroups is generically simple. That is with asymptotic density equal to one a randomly chosen finitely generated subgroup has a particular well-known and easily analyzed structure. For example a result of D. B. A. Epstein says that a finitely generated subgroup of GL(n,R) is generically a free group. We say that a group G has the generic fre...