NILPOTENT COVERINGS OF FINITE GENERAL LINEAR GROUPS

A subset X of group G is said to be non-nilpotent if for any two distinct elements x and y in X, hx; yi is a non-nilpotent subgroup of G. If for any other non-nilpotent subset X0 in G, jXj ¸ jX0j, then X is said to be a maximal non-nilpotent subset and the cardinality of this subset is denoted by !(NG). Using nilpotent nilpotentizers we find a lower bound for the cardinality of a maximal non-nilpotent subset of a some finite group.