Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123220220701Minimal generating sequences of F-subgroups496016359110.30504/jims.2022.367761.1079ENA.LucchiniDepartment of Mathematics, Tullio Levi Civita, University of Padova, Italy.0000-0002-2134-4991Journal Article20221030The behaviour of generating sets of finite groups has been widely studied, from several points of view. The purpose of this note is to investigate what happens when, instead of sets of elements generating a group, sets of subgroups belonging to a prescribed family are considered. Some known results on generating set can be extended and generalized, using similar arguments and techniques, but interesting open questions also arise.https://jims.ims.ir/article_163591_7a442fe33987570e188f5bf7173ddc53.pdf