A class of generalised finite T-groups

Let F be a formation (of finite groups) containing all nilpotent groups such that any normal subgroup of any T-group in F and any subgroup of any soluble T-group in F belongs to F. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. Named after Kegel, a subgroup U of a finite group G is called a K- F-subnormal subgroup of G if either U=G or U=U0?U1???Un=G such that Ui?1 is either normal in Ui or Ui1 is F-normal in Ui, for i=1,2,...,n. We call a finite group G a TF-group if every K- F-subnormal subgroup of G is normal in G. When F is the class of all finite nilpotent groups, the TF-groups are precisely the T-groups. The aim of this paper is to analyse the structure of the TF-groups and show that in many cases TF is much more restrictive than T. © 2011 Elsevier Inc. The authors would like to thank the referee and Ramon Esteban-Romero for useful and insightful comments. The first and the third authors have been supported by the grant MTM2007-68010-C03-02 from Ministerio de Educacion y Ciencia (Spain) and FEDER (European Union). Ballester-Bolinches, A.; Feldman ., A.; Pedraza Aguilera, MC.; Ragland., M. (2011). A class of generalised finite T-groups. Journal of Algebra. 333(1):128-138. https://doi.org/10.1016/j.jalgebra.2011.02.018