Jordan permutation groups and limits of ????-relations

Binary Relations and Permutation Groups

We discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surpri...

Generalized Covering Groups and Direct Limits

Orbit equivalence and permutation groups defined by unordered relations

For a set Ω an unordered relation on Ω is a family R of subsets of Ω . If R is such a relation we let G(R) be the group of all permutations on Ω that preserve R, that is g belongs to G(R) if and only if x ∈R implies x ∈R. We are interested in permutation groups which can be represented as G= G(R) for a suitable unordered relation R on Ω . When this is the case, we say that G is defined by the r...

Finitely Presented Algebras and Groups Defined by Permutation Relations *

The class of finitely presented algebras over a field K with a set of generators a1, . . . , an and defined by homogeneous relations of the form a1a2 · · · an = aσ(a)aσ(2) · · · aσ(n), where σ runs through a subset H of the symmetric group Sym n of degree n, is introduced. The emphasis is on the case of a cyclic subgroup H of Sym n of order n. A normal form of elements of the algebra is obtaine...

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...