(untitled) - Ballester-Bolinches, Adolfo; Kamornikov, Sergey; Pérez-Calabuig, Vicent; Yi, Xiaolan (Comptes Rendus. Mathématique, 2025)
Let $σ = \bigl \lbrace σ _i \;\big \vert \; i \in I\bigr \rbrace $ be a partition of the set of all primes with $σ \ne \lbrace \mathbb{P}\rbrace $. Problem 19.84 of the Kourovka Notebook shows that a $σ $-analogue of the classical Wielandt criterion of subnormality is not true in general. In this paper, we prove a Wielandt-type $σ $-subnormality criterion in terms of the Baer–Suzuki width of the class of all $σ _0$ groups, where $σ _0$ is the member of $σ $ such that $2 \in σ _0$.