On the II-property of subgroups of finite groups

A subgroup H of a finite group G is said to satisfy the -property in G if every prime dividing also divides the order of , for every G-chief factor L/K of G. The -property is a subgroup embedding property of arithmetical character introduced in Li (J. Algebra 334:321-337, 2011) that gathers common properties of many other well-known subgroup embeddings (most of them of normal type) and allows us to glimpse common behaviors to all of them. The aim of this note is to prove that a finite group G is soluble if and only if in G all maximal subgroups satisfy the -property in G. This is the answer to a question posed by Li (J. Algebra 334:321-337, 2011, Question 5.2).