On the theory of characters of π-separable groups
Irini Pimenidou · Warwick Research Archive Portal (University of Warwick) · 1988
In this thesis we demonstrate the existence of certain Fong characters that behave well with respect to subnormal subgroups of a π-separable group G, thereby answering a question of I. M. Isaacs. We also prove that any π-separable group G has a set of X-injectors, where X is the class of groups that can be written as the direct product of their Hall π- and Hall π'- subgroups. Further we prove that for all χ ε Irr(G) there exist a unique normal subgroup FN(χ) of G which is maximal with the property that every irreducible constituent of χFN(χ) is π-factorable. We then show that ȠFN(χ) = Gx, where Gx is the X-radical of G. Finally we construct a set χεIrr(G).