Characteristic covering numbers of finite simple groups

In the past few decades there has been considerable interest in word maps on groups with emphasis (non-abelian) finite simple groups. Various asymptotic results (holding for sufficiently large groups) have obtained. More recently non-asymptotic all emerged, particular words (commutators and certain power words) which are not an identity of any group. this paper we initiate a systematic study above property. particular, show that, if $$w_1, \ldots , w_6$$ group, then $$w_1(G)w_2(G) w_6(G) = G$$ G. Consequently, every w, either $$w(G)^6 groups, or $$w(G)=1$$ some These theorems follow from more general obtain characteristic collections their covering numbers, independent additional applications.