A classification of some insoluble varieties of groups of exponent four

We classify the subvarieties of the variety B-4 boolean AND C-4 of all 4-Engel groups of exponent 4 which contain the proper subvariety defined by M. Quick (J. London Math. Soc, to appear), 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. (C) 1997 Academic Press.