Levi-Properties Generated by Varieties
نویسنده
چکیده
Levi-properties were first introduced by L. C. Kappe and are modeled after groups investigated by F. W. Levi where conjugates commute. 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.
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