A classification of tetravalent one-regular graphs of order 3p²
A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, tetravalent one-regular graphs of order 3p², where p is a prime, are classified.
A classification of the nilpotent triangular matrices
A closed category of reflexive topological abelian groups
A closure condition which is equivalent to the Thomsen condition in quasigroups.
In this note it is shown that the closure condition, X1Y2 = X2Y1, X1Y4 = X2Y3, X3Y3 = X4Y1 --> X4Y2 = X3Y4, (and its dual) is equivalent to the Thomsen condition in quasigroups but not in general. Conditions are also given under which groupoids satisfying it are principal homotopes of cancellative, abelian semigroups, or abelian groups.
A coarse convergence group need not be precompact
A Cohomological Property of Regular p-Groups.
A combinatorial formula for Kazhdan-Lusztig polynomials.
A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of the symmetric group.
A combinatorial problem in infinite groups.
A Combinatorial Proof of the Existence of the Generic Hecke Algebra and R-Polynomials.
A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A combinatorial theorem on -power-free words and an application to semigroups
A combinatorial theory of Grünbaum's new regular polyhedra, Part I: Grünbaum's new regular polyhedra and their automorphism group.
A common generalization of Kelley's theorem (concerning measures on Boolean algebra) and on von Neumann's minimax theorem
A comparison of some generalizations of Green's relations.
A completion theorem for finitely generated commutative semigroups.
A computation concerning doubly transitive permutation groups.
A computational verification of Alperin's weight conjecture for groups of small order and their prime fields.
A computer algebra solution to a problem in finite groups.
We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.
A concept of variety for regular biordered sets.