The restricted Burnside problem for Moufang loops

We prove that for positive integers $m \geq 1, n \geq 1$ and a prime number $p \neq 2,3$ there are finitely many finite m-generated Moufang loops of exponent $p^n$ .

Burnside-type problems in discrete geometry

The paper is concerned with systems of incidence involving a space of points X and lines consisting of q points each. A free space X is defined. For a space X an analogue of the Burnside problem (solved in the negative) and an analogue of the weakened Burnside problem are formulated. In the case q = 3 the positive answer to the analogue of the weakened Burnside problem is equivalent to the existence of a universal finite geometry.

Residuated Lattices, Regular Languages, and Burnside Problem

In this talk we are going to explore an interesting connection between the famous Burnside problem for groups, regular languages, and residuated lattices.

Restricted Burnside problem for semigroups and its application to language theory

In this paper, we introduce the concept of strongly torsion property of semigroups. Then we prove that the strongly torsion property of a semigroup is a necessary and sufficient condition for a finitely generated semigroup to be finite, and hence, the strongly torsion property is equivalent to the torsion property together with the permutation property for the class of finitely generated semigroups. Finally, we give an application of our main result to language theory. A question proposed in [H. Prodinger, Congruences defined by languages and filters, Inf. Control 44 (1980) 36–46] is consequently answered.