An extension of a theorem by B.H. Neumann on groups with boundedly finite conjugacy classes

Kurdachenko, L. A. ; Muñoz-Escolano, J. M. (Universidad de Zaragoza) ; Otal, J. (Universidad de Zaragoza)

Resumen: The source of this paper is a classical theorem by B. H. Neumann on groups whose conjugacy classes are boundedly finite. In a natural way this leads to the study of groups with restrictions on the normal closures of their cyclic subgroups. More concretely, in this paper we study groups G such that the normal closure of every cyclic subgroup
has a divisible Chernikov G-invariant subgroup D of minimax rank r such that gD has at most b conjugates in the factorgroup G/D. We prove that such groups are Chernikov-by-abelian and bound their invariants in terms of r and b only.

Idioma: Inglés

DOI: 10.1007/s00032-012-0172-0

Año: 2012

Publicado en: Milan Journal of Mathematics 80, 1 (2012), 227-241
ISSN: 1424-9286

Factor impacto JCR: 0.467 (2012)

Categ. JCR: MATHEMATICS rank: 194 / 295 = 0.658 (2012) - Q3 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 197 / 247 = 0.798 (2012) - Q4 - T3

Tipo y forma: Article (Published version)

Área (Departamento): Área Didáctica Matemática (Dpto. Matemáticas)
Área (Departamento): Área Algebra (Dpto. Matemáticas)