Bounds on the fitting length of finite soluble groups with supersoluble Sylow normalisers

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...

Finite Groups with p-Sylow Coverings

Languages Recognized by Finite Supersoluble Groups

In this paper, we give two descriptions of the languages recognized by finite supersoluble groups. We first show that such a language belongs to the Boolean algebra generated by the modular products of elementary commutative languages. An elementary commutative language is defined by a condition specifying the number of occurrences of each letter in its words, modulo some fixed integer. Our sec...

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.