Levi-properties generated by varieties
Robert Fitzgerald Morse · Contemporary mathematics - American Mathematical Society · 1994
Abstract. Levi-properties were first introduced by L. C. Kappe and are modeled after groups investigated by F. W. Levi where conjugates com-mute. Let X be a group theoretic class. A group is in the derived class L(X) if the normal closure of each element in the group is an X-group. The property of being in the class L (X) is called the Levi-property generated by X. In the case where X is a variety, we show that L(X) is also a variety. Given the laws defining any variety V, the laws defining a variety W can be exactly stated such that L(V) ≤ W. However, there exists a variety V such that L(V) < W. Our investigations show for varieties defined by outer commutator laws, denoted by O, the varieties L(O) and W coincide. 1.