On 𝔉-normalizers
Ti Yen · Proceedings of the American Mathematical Society · 1970
The concept of system normalizers of a finite solvable group is generalized to any saturated formation F \mathfrak {F} . Given a Sylow system Σ \Sigma of the finite solvable group G G and an F \mathfrak {F} -projector V V of G G reducing Σ \Sigma , a sequence { H i } \{ {H_i}\} of subgroups H i {H_i} , is constructed such that (i) each H i {H_i} reduces Σ \Sigma , and (ii) the F \mathfrak {F} -normalizers of Σ ∩ H i \Sigma \cap {H_i} in H i {H_i} converge to V V