Subcartesian products of finitely many finite algebras

Finite Models and Finitely Many

This paper is a survey of results on nite variable logics in nite model theory. It focusses on the common underlying techniques that unite many such results.

Products of Many Sorted Algebras

For simplicity we follow the rules: I, J denote sets, A, B denote many sorted sets of I, i, j, x are arbitrary, and S denotes a non empty many sorted signature. A set has common domain if: (Def.1) For all functions f , g such that f ∈ it and g ∈ it holds dom f = dom g. Let us mention that there exists a set which is functional and non empty and has common domain. The following proposition is tr...

Finite Models and Finitely Many Variables

More on Products of Many Sorted Algebras

This article is continuation of an article defining products of many sorted algebras [11]. Some properties of notions such as commute, Frege, Args() are shown in this article. Notions of constant of operations in many sorted algebras and projection of products of family of many sorted algebras are defined. There is also introduced the notion of class of family of many sorted algebras. The main ...

On solubility of groups with finitely many centralizers

For any group G, let C(G) denote the set of centralizers of G.We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n.In this note, we prove that every finite Cn-group with n ≤ 21 is soluble andthis estimate is sharp. Moreover, we prove that every finite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashrafi in ...