Título:	Finite groups in which every commutator has prime power order
Autor(es):	Souza, Mateus Figueiredo de Shumyatsky, Pavel
ORCID:	https://orcid.org/0000-0002-4976-5675
Afiliação do autor:	Universidade de Brasília, Departamento de Matemática Universidade de Brasília, Departamento de Matemática
Assunto:	Grupos finitos Comutadores
Data de publicação:	27-jun-2024
Editora:	Elsevier
Referência:	SOUZA, Mateus Figueiredo de; SHUMYATSKY, Pavel. Finite groups in which every commutator has prime power order. Journal of Algebra, [S. l.], v. 658, p. 779–797, 2024. DOI: https://doi.org/10.1016/j.jalgebra.2024.06.014. Disponível em: https://www.sciencedirect.com/science/article/pii/S0021869324003508?via%3Dihub. Acesso em: 30 jun. 2025.
Abstract:	Finite groups in which every element has prime power order (EPPO-groups) are nowadays fairly well understood. For instance, if G is a soluble EPPO-group, then the Fitting height of G is at most 3 and |π(G)| 2 (Higman, 1957). Moreover, Suzuki showed that if G is insoluble, then the soluble radical of G is a 2-group and there are exactly eight nonabelian simple EPPO-groups. In the present work we concentrate on finite groups in which every commutator has prime power order (CPPO-groups). Roughly, we show that if G is a CPPO-group, then the structure of G is similar to that of an EPPO-group. In particular, we show that the Fitting height of a soluble CPPOgroup is at most 3 and |π(G)| 3. Moreover, if G is insoluble, then R(G) is a 2-group and G/R(G) is isomorphic to a simple EPPO-group.
Unidade Acadêmica:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
Programa de pós-graduação:	Programa de Pós-Graduação em Matemática
DOI:	https://doi.org/10.1016/j.jalgebra.2024.06.014
Versão da editora:	https://www.sciencedirect.com/science/article/pii/S0021869324003508
Aparece nas coleções:	Artigos publicados em periódicos e afins

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