Endomorphism monoid and automorphism group of residually finite and profinite quandles

Abstract

We explore residually finite and profinite quandles. We prove that the endomorphism monoid and the automorphism group of finitely generated residually finite quandles are residually finite. In fact, we establish the similar result for a broad class of residually finite quandles. We provide a topological characterization of profinite quandles. We establish necessary and sufficient conditions for profinite quandles ensuring that their endomorphism monoids and automorphism groups are profinite.