An Arad and Fisman&apos
[EN] 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 boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian simple group. We demonstrate that, in fact, < A > = < B &...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/194638 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/194638 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Conjugacy classes Products of conjugacy classes Solvability criterium MATEMATICA APLICADA |
| Resumo: | [EN] 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 boolean OR B or AB = A(-1) boolean OR 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 p-nilpotent. 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. |
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