Orbits of maximal invariant subgroups and solvability of finite groups
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Orbits of maximal invariant subgroups and solvability of finite groupsDate
2019-08-13Publisher
ElsevierBibliographic citation
SHAO, Changguo; BELTRÁN, Antonio. Orbits of maximal invariant subgroups and solvability of finite groups. Journal of Algebra, 2019, 539: 177-200.Type
info:eu-repo/semantics/articlePublisher version
https://www.sciencedirect.com/science/article/pii/S0021869319304491Version
info:eu-repo/semantics/acceptedVersionSubject
Abstract
Let A and G be finite groups having coprime orders and suppose that A acts on G via automorphisms. We give some solvability criteria for G according to the number of orbits that appear by the action of the fixed point ... [+]
Let A and G be finite groups having coprime orders and suppose that A acts on G via automorphisms. We give some solvability criteria for G according to the number of orbits that appear by the action of the fixed point subgroup on the set of maximal A-invariant subgroups of G, and likewise, on the set of non-nilpotent maximal A-invariant subgroups. We also obtain some characterizations and further structure properties of these groups. In the course of our study we prove an independent result concerning maximal factorizations of classical simple groups. [-]
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