An Arad and Fisman’s Theorem on Products of Conjugacy Classes Revisited
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Títol
An Arad and Fisman’s Theorem on Products of Conjugacy Classes RevisitedData de publicació
2022Editor
SpringerCita bibliogràfica
BELTRÁN, Antonio; FELIPE, María José; MELCHOR, Carmen. An Arad and Fisman’s Theorem on Products of Conjugacy Classes Revisited. Mediterranean Journal of Mathematics, 2022, 19.6: 257.Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
A theorem of Z. Arad and E. Fisman establishes that if A and
B are two non-trivial conjugacy classes of a finite group G such that
either AB = A ∪ B or AB = A−1 ∪ B, then G cannot be a non-abelian
simple group. We ... [+]
A theorem of Z. Arad and E. Fisman establishes that if A and
B are two non-trivial conjugacy classes of a finite group G such that
either AB = A ∪ B or AB = A−1 ∪ B, then G cannot be a non-abelian
simple group. We demonstrate that, in fact, A = B is solvable, the
elements of A and B are p-elements for some prime p, and A is pnilpotent. Moreover, under the second assumption, it turns out that A =
B. This research is done by appealing to recently developed techniques
and results that are based on the Classification of Finite Simple Groups. [-]
Publicat a
Mediterranean Journal of Mathematics, 2022, 19.6: 257Entitat finançadora
Ministerio de Ciencia, Innovación y Universidades | Generalitat Valenciana | National Nature Science Fund of China | Universitat Jaume I
Codi del projecte o subvenció
PGC2018-096872-B-I00 | CIAICO/2021/163 | 12071181 | UJI-B2019-03
Drets d'accés
info:eu-repo/semantics/openAccess
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