Let Γ be a limit group, S ⊂ Γ a non-trivial subgroup, and N the normaliser of S. If H1(S,Q) has finite Q-dimension, then S is finitely generated and either N/S is finite or N is abelian. This result has applications to the study of subdirect products of limit groups. Limit groups (or ω-residually free groups) have received a good deal of attention in recent years, largely due to the work of Z. ...

We explore an elementary construction that produces finitely presented groups with diverse homological finiteness properties – the binary subgroups, $B(\Sigma,\mu)\<G\_1\times\dots\times G\_m$. These full subdirect products require strikingly few generators. If each $G\_i$ is presented, $B(\Sigma,\mu)$ presented. When are non-abelian limit (e.g. free or surface groups), provide new examples of ...

In this paper we make an algebraic study of the variety of M V * –algebras introduced by C. C.Chang as an algebraic counterpart for a logic with positive and negative truth values. We build the algebraic theory of M V * –algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in –groups. The main results are a subd...

The purpose of this paper is to describe structural properties of automata whose transition semigroups have a zero, left zero, right zero or bi-zero, or are nilpotent extensions of rectangular bands, left zero bands or right zero bands, or are nilpotent. To describe the structure of these automata we use various well-known decomposition methods of automata theory – direct sum decompositions, su...