The 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.
Minimal generating sequences of F-subgroups
Lucchini A.
2022
Abstract
The 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.File in questo prodotto:
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JIMS_Volume 3_Issue 2_Pages 49-60.pdf
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