Squarefree Polynomials over Finite Fields and Regular Semisimple Classes of Certain Classical Groups

LetGbePSLn(q),PSUn(q),Sp2n(q) orPSp2n(q), whereqis a power of the primep. Using results on the numbers of special squarefree polynomials over finite fields, we describe and count the conjugacy classes ofp′-elements with abelian centralizers inG. Similar results are obtained for the semisimple orbits ofGon the corresponding finite Lie algebras.