Abstract Classical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent coincide with projectors and covering they form a non-empty conjugacy class in groups. This paper presents an extension these facts to $$\pi $$ π -separable groups, for sets primes ...

This paper describes algorithms for constructing a Hall n-subgroup H of a finite soluble group G and the normaliser No(H). If G has composition length n, then H and No(H ) can be constructed using O(n ~ log IGI) and O(n ~ log IGI) group multiplications, respectively. These algorithms may be used to construct other important subgroups such as Carter subgroups, system normalisers and relative sys...

There is a large collection of e ective algorithms for computing information about nite soluble groups. The success in computation with these groups is primarily due to a computationally convenient representation of them by means of (special forms of) power conjugate presentations. A notable omission from this collection of algorithms is an e ective algorithm for computing the automorphism grou...