Levi-properties generated by varieties [unknown]

Robert Fitzgerald Morse
1994 Contemporary Mathematics   unpublished
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
more » ... 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. 1991 Mathematics Subject Classification. Primary 20E10 20F12.
doi:10.1090/conm/169/01675 fatcat:n452stwpgzgdpeogrhunxxpnxu