Artículo
On localizations of quasi-simple groups with given countable center
Autor/es | Flores Díaz, Ramón Jesús
![]() ![]() ![]() ![]() ![]() ![]() ![]() Rodríguez, José Luis |
Departamento | Universidad de Sevilla. Departamento de Geometría y Topología |
Fecha de publicación | 2020-10-22 |
Fecha de depósito | 2023-04-14 |
Publicado en |
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Resumen | A group homomorphism i:H→G is a localization of H, if for every homomorphism φ:H→G there exists a unique endomorphism ψ:G→G such that iψ=φ (maps are acting on the right). Göbel and Trlifaj asked in [18, Problem 30.4(4), ... A group homomorphism i:H→G is a localization of H, if for every homomorphism φ:H→G there exists a unique endomorphism ψ:G→G such that iψ=φ (maps are acting on the right). Göbel and Trlifaj asked in [18, Problem 30.4(4), p. 831] which abelian groups are centers of localizations of simple groups. Approaching this question we show that every countable abelian group is indeed the center of some localization of a quasi-simple group, i.e., a central extension of a simple group. The proof uses Obraztsov and Ol'shanskii's construction of infinite simple groups with a special subgroup lattice and also extensions of results on localizations of finite simple groups by the second author and Scherer, Thévenaz and Viruel. |
Cita | Flores Díaz, R.J. y Rodríguez, J.L. (2020). On localizations of quasi-simple groups with given countable center. Groups Geometry and Dynamics, 14 (3), 1023-1042. https://doi.org/10.4171/GGD/573. |
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