Finite groups generated by subnormal T-subgroups

John Cossey
1995 Glasgow Mathematical Journal  
1. Introduction. Our aim in this paper is to investigate the restrictions placed on the structure of a finite group if it can be generated by subnormal T-subgroups (a T-group is a group in which every subnormal subgroup is normal). For notational convenience we denote by % the class of finite groups that can be generated by subnormal T-subgroups and by 3if* the subclass of 3{ of those finite groups generated by normal 7-subgroups; and for the remainder of this paper we will only consider finite
more » ... nly consider finite groups. T-groups may be regarded as a generalisation of abelian groups. We know that a group generated by subnormal abelian subgroups is nilpotent; and a group generated by normal abelian subgroups has class bounded by the number of abelian normal subgroups needed to generate it. We will be seeking results analogous to these for groups in % and 3K*. We begin by considering soluble ^f-groups. One of the basic properties of 7-groups is that they are supersoluble and we will show that this property nearly carries over to 3if-groups; indeed X-groups of odd order are supersoluble, as are soluble $f*-groups.
doi:10.1017/s0017089500031645 fatcat:vb6r4qlswvfk5jurwus6v3f7xa