Inductor Maps Of Character Triples

In this thesis,we study the correspondence between the inductors and restrictors of character triples,and introduce the inductor maps of character triples.The images of inductor maps are described,and a bijection between the set of inductors and the set of inductors of covering subtriples is established.The covering subtriples is a special kind of restrictors.Some basic properties of the map are investigated,and we generalize some known results about the inductors.The main conclusions of this thesis are as follows:Theorem A Let T be a character triple,and R be a restrictor of T.Then there is a function f : Ind(T)-? Ind(R),f(T?)= R?,preserving the index of inductors,i.e.,|T : T?| = |R : R?|.Theorem B Let T =(G,N,?)be a character triple and R =(H,M,?)be a restrictor of T.If R?=(H?,M?,??)is an inductor of R,such that(M?,??)is an inductive source of N,then there exists an inductor T?=(G?,N?,??)of T such that R?is a restrictor of T?,or equivalently,f(T?)= R?.Theorem C Let T be a character triple.If R is a covering subtriple of T,then the map f : Ind(T)-? Ind(R)is a bijection,and the image R?= f(T?)of any inductor T?? Ind(R)is also a covering subtriple of T?.