Abstract

THEOREM 3. A variety of groups is Cross if and only ;f it is generated by a finite group. Theorem 1 is an immediate consequence of this. Theorem 2 is trivial if B is contained in ‘u and, in particular, if B is not critical. If B is critical, then it has a unique minimal normal subgroup M, and the proof divides into two according as M is or is not abelian. In either case, it is sufficient to prove that U(n) satisfies the conditions for a Cross

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