David P. Cargo, Warwick de Launey, Martin W. Liebeck, Richard M. Stafford
September 19, 2008
In this paper, we consider finite groups G satisfying identities of the form . We focus on identities with r small, , and all coprime to the order of G . We show that for r = 2,3 and 5, G must be nilpotent. We also classify for r = 4,6 and 7, the special identities which can hold in non-nilpotent groups. Finally, we show that for r < 30, the group G must be solvable.