On powers of conjugacy classes in finite groups
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Título
On powers of conjugacy classes in finite groupsAutoría
Fecha de publicación
2022-03-17Editor
De GruyterISSN
1433-5883; 1435-4446Cita bibliográfica
Beltrán, Antonio. "On powers of conjugacy classes in finite groups" Journal of Group Theory , no. (2022). https://doi.org/10.1515/jgth-2021-0156Tipo de documento
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info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
Let 𝐾 and 𝐷 be conjugacy classes of a finite group 𝐺, and suppose that we have
Kn=D∪D−1 for some integer n≥2. Under these assumptions, it was conjectured that ⟨K⟩ must be a (normal) solvable subgroup of 𝐺. ... [+]
Let 𝐾 and 𝐷 be conjugacy classes of a finite group 𝐺, and suppose that we have
Kn=D∪D−1 for some integer n≥2. Under these assumptions, it was conjectured that ⟨K⟩ must be a (normal) solvable subgroup of 𝐺. Recently R. D. Camina has demonstrated that the conjecture is valid for any n≥4, and this is done by applying combinatorial results, the main of which concerns subsets with small doubling in a finite group. In this note, we solve the case n=3 by appealing to other combinatorial results, such as an estimate of the cardinality of the product of two normal sets in a finite group as well as to some recent techniques and theorems. [-]
Entidad financiadora
Ministerio de Ciencia, Innovación y Universidades | Universitat Jaume I | National Natural Science Foundation of China | Generalitat Valenciana
Código del proyecto o subvención
PGC2018-096872-B-100 | UJI-B2019-03 | 12071181 | AICO/2020/298
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
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