International Journal of Algebra and Computation

In this paper, we detail the geometrical approach of small cancellation theory used by Delzant and Gromov to provide a new proof of the infiniteness of free Burnside groups and periodic quotients of torsion-free hyperbolic groups.

We extend the results of Ershov, Jaikin-Zaiprin, and Kassabov on property (T) to certain groups "coordinatized" by nonassociative algebras, thereby giving new examples of groups with property (T).

We consider the infinite dimensional Grassmann algebra E over a field F of characteristic 0 or p, where p > 2, and we compute its ℤ₂-graded Gelfand–Kirillov (GK) dimension as a ℤ₂-graded PI-algebra.

We generalize the notion of discriminator variety in such a way as to capture several varieties of algebras arising mainly from fuzzy logic. After investigating the extent to which this more general concept retains the basic properties of discriminator varieties, we give both an equational and a purely algebraic characterization of quasi-discriminator varieties. Finally, we completely describe the lattice of subvarieties of the pure pointed quasi-discriminator variety, providing an explicit equational base for each of its members.