Finite groups in which every commutator has prime power order

Souza, Mateus Figueiredo de; Shumyatsky, Pavel

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Campo DC	Valor	Idioma
dc.contributor.author	Souza, Mateus Figueiredo de	-
dc.contributor.author	Shumyatsky, Pavel	-
dc.date.accessioned	2025-09-24T10:45:53Z	-
dc.date.available	2025-09-24T10:45:53Z	-
dc.date.issued	2024-06-27	-
dc.identifier.citation	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.	pt_BR
dc.identifier.uri	http://repositorio.unb.br/handle/10482/52494	-
dc.language.iso	eng	pt_BR
dc.publisher	Elsevier	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Finite groups in which every commutator has prime power order	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Grupos finitos	pt_BR
dc.subject.keyword	Comutadores	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.jalgebra.2024.06.014	pt_BR
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0021869324003508	pt_BR
dc.description.abstract1	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.	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0002-4976-5675	pt_BR
dc.contributor.affiliation	Universidade de Brasília, Departamento de Matemática	pt_BR
dc.contributor.affiliation	Universidade de Brasília, Departamento de Matemática	pt_BR
dc.description.unidade	Instituto de Ciências Exatas (IE)	pt_BR
dc.description.unidade	Departamento de Matemática (IE MAT)	pt_BR
dc.description.ppg	Programa de Pós-Graduação em Matemática	pt_BR
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