We classify the real and strongly real conjugacy classes in GLn(q), SLn(q), PGLn(q), PSLn(q), and all quasi-simple covers of PSLn(q). In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes.

In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define a of elements full monomial group exploit this describe conjugacy classes centralisers group. We generalise their results wreath products whose base need not be finite top acts faithfully on set. parameterise such explicitly. For products, our approach yields efficient algorithms for finding conjugating ...