A computational method for determining the automorphism group of a finite solvable group

Abstract

This chapter discusses a computational method for determining the automorphism group of a finite solvable group. Many problems in the theory of finite groups, especially of the extension theory, depend on the knowledge of the structure of the automorphism group A(G) of a finite group G. A computer program for determining A(G) of a finite group G has been described in the chapter. With a view to the computational construction of A(G) it is profitable to develop systematically methods for determining A(G) by composition of allowable automorphisms of special subgroups of G.