Permutability of subgroups and $$\mathfrak{F}$$ -subnormality

σ-Subnormality in locally finite groups

“…Second, σ-residuals have very nice permutability properties. Using Lemma 3 (5) of [2], the argument in Lemma 3.3 of [6] proves the following result. Lemma 2.3 Let σ = {σ i : i ∈ I} be a partition of P and let G be a σ-soluble finite group.…”

$\mathfrak{F}$ -critical groups, $\mathfrak{F}$ -subnormal subgroups, and the generalised Wielandt property for residuals

“…To be a subgroup-closed Fitting formation is a necessary condition for a formation F to have the generalised Wielandt property for residuals as Kamornikov proved in [15]. For the sake of completeness, we include here a proof of this result.…”

“…Interesting results in this direction can be found in the papers of S.F. Kamornikov [15] and M.C. Pedraza-Aguilera, M.D.…”

On one problem in formation theory

“…By Theorem 2.1 in [1], F is a GWP-formation. Let G be an F-critical group having identity Frattini subgroup.…”

“…In [1], we described the essential properties of GWP-formations. It was proved in particular that each GWP-formation is a hereditary lattice Fitting formation and the sufficiently wide class of GWPformations was distinguished.…”