For each k = 0, 1, 2, . . . we define an equivalence relation called k-quasi-isotopy on the set of classical links in R3 up to isotopy in the sense of Milnor (1957), such that all sufficiently close approximations of a topological link are k-quasi-isotopic. Whereas 0-quasi-isotopy coincides with link homotopy, 1-quasi-isotopy is not implied by concordance, with aid of the generalized (lk 6= 0) ...

Let S be a finite set of powers of p containing 1. It is known that for some choices of S, if P is a finite p-group whose set of character degrees is S, then the nilpotence class of P is bounded by some integer that depends on S, while for some other choices of S such an integer does not exist. The sets of the first type are called class bounding sets. The problem of determining the class bound...

We give a deterministic polynomial-time algorithm to check whether the Galois group Gal (f) of an input polynomial f(X) ∈ Q[X] is nilpotent: the running time is polynomial in size (f). Also, we generalize the Landau-Miller solvability test to an algorithm that tests if Gal (f) is in Γd: this algorithm runs in time polynomial in size (f) and n d and, moreover, if Gal (f) ∈ Γd it computes all the...

Dual numbers, split-quaternions, split-octonions, and other number systems with nilpotent spaces have received sporadic yet persistent interest, beginning from their roots in the 19th century, to more recent attention in connection with supersymmetry in physics. In this paper, a number system in the 2D plane is investigated, where the squares of its basis elements p and q each map into the coor...

A sectionally complemented modular lattice L is coordinatizable if it is isomorphic to the lattice L(R) of all principal right ideals of a von Neumann regular (not necessarily unital) ring R. We say that L has a large 4-frame if it has a homogeneous sequence (a0, a1, a2, a3) such that the neutral ideal generated by a0 is L. Jónsson proved in 1962 that if L has a countable cofinal sequence and a...

In the early nineteen eighties, Gunnar Carlsson proved the Segal conjecture on the stable cohomotopy of the classifying space BG of a finite group G. This led to an algebraic description of the ring of stable self-maps of BG as a suitable completion of the “double Burnside ring”. The problem of understanding the primitive idempotent decompositions of the identity in this ring is equivalent to u...

The assignment (nonstable K0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (i) There is no functor Γ, from simplicial monoids with order-unit with normalized positive homomorphisms t...

Introduction. If P is a ring and M a left P-module, then homological algebra attaches three dimensions to M, projective, weak, and injective(1)By taking the supremum of one of these dimensions as M ranges over all left P-modules, one obtains one of the left "global" dimensions of R. Auslander and Buchsbaum [3] and, subsequently, Serre [14], found it relevant and fruitful, in the study of commut...

All groups considered are finite. Given a group G, the Frattini subgroup of G, Q(G) is defined to be the intersection of all maximal subgroups of G. There has been much interest in generalizing the Frattini subgroup in various ways, and in investigating their influence on the structure of the group (see [3,.5,8,12,13]). These generalizations were done taking into account the following question:...