Bryce, Robert2015-12-070004-9727http://hdl.handle.net/1885/19788A special case of the main result is the following. Let G be a finite, non-supersoluble group in which from arbitrary subsets X, Y of cardinality n we can always find x ∈ X and y ∈ Y generating a supersoluble subgroup. Then the order of G is bounded b200610.1017/S00049727000356682015-12-07