A JUST NON-FINITELY BASED VARIETY OF BIGROUPS

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.

Acknowledgments

Notes

^*The first author was supported by NSERC, Canada.