Products of conjugate permutations

Abstract

If s, pβSv, \s S \p and \p is infinite, then s is a product of 4 elements each conjugate to p. Furthermore, 4 is minimal with this property. The latter follows by examining s = (123) and any permutation p containing only transpositions (without fixed points) in its disjoint cycle decomposition, cf. G. Moran [6, p. 76] and [4, p. 288, 289]. If p is odd and s is even (with finite supports), then obviously s $ (pή and similar examples with finite | p | show