Character Degrees and Direct Products

The principal object of this book is to discuss in detail the influence of character degrees on the structure of finite groups especially solvable groups. ¿Character ¿¿theory ¿has ¿¿very ¿strong ¿interplay ¿with group ¿structure. In the last two decades,¿ a number of papers has appeared that indicates the existence of a connection ¿between the character degree set of a finite group and its¿ ¿structure¿. ¿It is not difficult to see that the character degree set ¿of a finite group does not completely determine the structure of the¿ ¿group¿, ¿and in fact¿, ¿it often gives us little information about the¿ ¿structure of the group¿. In ¿this book, ¿we present ä ¿problem ¿arising ¿in a ¿particular character ¿degree ¿set. ¿We look at a particular character degree set and we ¿obtain strong structural information about the group more than what ¿we expected¿. ¿This gives more evidence to the existence of a deep¿ ¿connection between the structure of a group and its character degree ¿set if this set is reasonably specified. This book will be useful to graduate students and researchers providing an up-to-date account of character theory of finite groups and related topics.