Abstract
A bigroup is a pair (H, π) consisting of a group H and an idempotent endomorphism π of H. One can consider π as a unary operation on H so a bigroup is a universal algebra. The aim of our paper is to construct the first example of a just non-finitely based variety of bigroups i.e. a variety which is non-finitely based but all whose proper subvarieties are finitely based. There is a close similarity between varieties of bigroups and varieties of groups so we hope that our result could help to construct a just non-finitely based variety of groups. *The first author was supported by NSERC, Canada.
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