in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

Fate maps are required to address questions about the commitment and differentiation of precardiac cells. Here, we report a detailed study of the precardiac cells located at the level of the primitive streak, employing different experiments with a variety of techniques combining double transplantations, microinjections and immunocytochemistry. Most cells of the more rostral segments of the prim...

A group G of permutations of a set Ω is primitive if it acts transitively on Ω, and the only G-invariant equivalence relations on Ω are the trivial and universal relations. A graph Γ is primitive if its automorphism group acts primitively on its vertex set. A graph Γ has connectivity one if it is connected and there exists a vertex α of Γ, such that the induced graph Γ \ {α} is not connected. I...

For a prime power q > 1 and an integer n ≥ 2 we consider the extension Fqn/Fq of Galois fields together with a cyclic Fq-vector space endomorphism τ . An element of Fqn is called a primitive τ-generator over Fq provided it generates the multiplicative group of Fqn , as well as the additive group of Fqn regarded as an Fq[x]-module with respect to τ . The notion of a primitive τ -generator genera...

and call it the essential weight of the partition μ. For our purpose it is convenient to ignore the parts equal to 1 in the partition because an element like (1, 2, 3) ∈ S3 is also an element of bigger symmetric groups. So we write μ = 22 , ..., nn for a partition and the corresponding class Cμ is a class of an arbitrary symmetric group Sn with n ≥ W (μ) depending on the context, i.e. C2 denote...

We generalise the group theoretic notion of a primitive permutation representation to inverse monoids and so obtain a notion of a primitive representation by partial permutations. Such representations are shown to be determined by what we call essentially maximal proper closed inverse submonoids. Such submonoids in the case of the polycyclic inverse monoids (also known as Cuntz inverse semigrou...

Given matrices A and B shift equivalent over a dense subring R of R, with A primitive, we show that B is strong shift equivalent over R to a primitive matrix. This result shows that the weak form of the Generalized Spectral Conjecture for primitive matrices implies the strong form. The foundation of this work is the recent result that for any ring R, the group NK1(R) of algebraic K-theory class...