Jake Zimmermann Simmons, Department of Pure Mathematics, University of Waterloo
"An example of a variety which is locally finite and residually finite but not residually < N for any natural number N (and also unfortunately not of finite type)"
We will construct an example of a variety, which is locally finite, and residually finite, but not residually < N for any natural number N, that is a combination of that given by Quackenbush and Abakumov et al. This is done by taking a set of cycles of prime cardinality and then extrapolating key sentences that they satisfy to the set of indirectly irreducable algebras in the variety that they generate in order to see that they all must be finite. It then remains to show that these the variety generated by these cycles is locally finite which is done by examining finitely generated free algebras in the variety and showing that they are finite.
MC 5479