Soluble groups with a finite rewriting system

Constructing Normalisers in Finite Soluble Groups

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...

Computing automorphisms of finite soluble groups

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...

Finite groups with three relative commutativity degrees

‎‎For a finite group $G$ and a subgroup $H$ of $G$‎, ‎the relative commutativity degree of $H$ in $G$‎, ‎denoted by $d(H,G)$‎, ‎is the probability that an element of $H$ commutes with an element of $G$‎. ‎Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$‎. ‎It is shown that a finite group $G$ admits three relative commutativity degrees if a...

Finite Groups with p-Sylow Coverings

A Family of Dominant Fitting Classes of Finite Soluble Groups

In this paper a large family of dominant Fitting classes of finite soluble groups and the description of the corresponding injectors are obtained. Classical constructions of nilpotent and Lockett injectors as well as p-nilpotent injectors arise as particular cases. 1994 Mathematics subject classification (Amer. Math. Soc.): primary 20D10.