J. Aust. Math. Soc.  76 (2004), 93-108
Fitting classes and lattice formations I

M. Arroyo-Jordá
  Departamento de Matemática Aplicada
  Universidad Politécnica de València
  Camino de Vera, s/n
  46071 València
M. D. Pérez-Ramos
  Departamento d'Àlgebra
  Universitat de València
  Doctor Moliner 50
  46100 Burjassot (València)

A lattice formation is a class of groups whose elements are the direct product of Hall subgroups corresponding to pairwise disjoint sets of primes. In this paper Fitting classes with stronger closure properties involving $\mathcal{F}$-subnormal subgroups, for a lattice formation $\mathcal{F}$ of full characteristic, are studied. For a subgroup-closed saturated formation $\mathcal{G}$, a characterisation of the $\mathcal{G}$-projectors of finite soluble groups is also obtained. It is inspired by the characterisation of the Carter subgroups as the $\mathcal{N}$-projectors, $\mathcal{N}$ being the class of nilpotent groups.
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