The topology of the relative character varieties of a quadruply-punctured sphere.
The totally simple quasigroups
The translational degree of a semigroup.
The translational hull in semigroups and rings.
The translational hull of a normal cryptogroup
The translational hull of a subsemigroup of a semilattice of groups.
The translational hull of an adequate semigroup.
The triangle and the open triangle
We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.
The triangle groups
The Union of Compact Subgroups of a Connected Locally Compact Group.
The uniqueness of groups of type J4.
The unit group of .
The universal group of homogeneous quotients.
The upper central series of some matrix groups
The upper triangular algebra loop of degree
A natural loop structure is defined on the set of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.
The varieties of languages corresponding to the varieties of finite band monoids.
The varieties of n-testable semigroups.
The variety generated by finite nilpotent monoids.
The variety of an indecomposable module is connected.
The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0
2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0. The algebras of this variety are left nilpotent of class not more than 3. We give a complete description of the vector space of multilinear identities in the language of representation theory of the symmetric group Sn and Young diagrams. We also show that the...