I. Martin Isaacs specializes in finite group theory and related topics. His principal interest is in the character theory of finite groups, and especially of those groups that have lots of normal subgroups.
        A character of a group is a certain type of function from the group into the complex numbers, Historically, characters have been used to prove theorems about groups. (The first major application, for example, was W. Burnside's proof that the order of a simple group cannot have just two prime divisors.) Isaacs is primarily interested in studying the subtle interplay between the characters of a group and the subgroup structure of the group.