A Classification of Some Insoluble Varieties of Groups of Exponent Four Original Research Article

We classify the subvarieties of the variety image4 ∩ image4of all 4-Engel groups of exponent 4 which contain the proper subvariety defined by[7], and from this we deduce a classification of all varieties of groups of exponent 4 which contain this subvariety. We also use the first classification to obtain a reduction for the finite basis problem for varieties of groups of exponent 4.