The semilattices of nilextensions of left groups and their varieties
Zhonghao Jiang, Liming Chen · Proceedings of the Japan Academy Series A Mathematical Sciences · 1998
In this paper, we characterize the semigroups which are the semilattices of nilextensions of left groups and prove that these semigroups form a variety defined by the equation (xy)( yx) (xy)O.Moreover, we obtain some decompositions of this variety by Mal'cev product and semidirect product.In particular, we prove that this variety is just the semidirect product G*R of the variety G of groups and the variety R of -trivial semi- groups.