THE PI-CHARACTER THEORY OF SOLVABLE-GROUPS

There is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Much of this structu re, which has no analog for general finite groups, becomes visible onl y when the characters of solvable groups are viewed from the perspecti ve of a particular set pi of prime numbers. This purely expository pap er discusses the foundations of this pi-theory and a few of its applic ations. Included are the definitions and essential properties of Gajen dragadkar's pi-special characters and their connections with the irred ucible pi-partial characters and their associated Fong characters. Inc luded among the consequences of the theory discussed here are applicat ions to questions about the field generated by the values of a charact ers about extensions of characters of subgroups and about M-groups.