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Multiplying a conjugacy class by its inverse in a finite group |
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| Authors: | Antonio Beltrán María José Felipe Carmen Melchor |
| Institution: | 1.Departamento de Matemáticas,Universidad Jaume I,Castellón,Spain;2.Instituto Universitario de Matemática Pura y Aplicada,Universidad Politécnica de Valencia,Valencia,Spain;3.Departamento de Matemáticas,Universidad Jaume I,Castellón,Spain |
| Abstract: | Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK?1 = 1 ∪ D ∪ D?1 with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical conditions on the class sizes determining the solvability and the structure of 〈K〉 and 〈D〉. |
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