Archivo por meses: abril 2015

Paper «On p-nilpotency of hyperfinite groups» published in Monatsh. Math.

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A. Ballester-Bolinches, S. Camp-Mora, and F. Spagnuolo

On p-nilpotency of hyperfinite groups

Monatsh. Math., 176(4) (2015), 497–502

http://dx.doi.org/10.1007/s00605-014-0633-3

Abstract

Let p be a prime. We say that class X of hyperfinite p-groups determines p-nilpotency locally if every finite group G with a Sylow p-subgroup P in X is p-nilpotent if and only if N_G(P) is p-nilpotent. The results of this paper improve a recent result of Kurdachenko and Otal and show that if a hyperfinite group G has a pronormal Sylow p-subgroup in X, then G is p-nilpotent if and only if N_G(P) is p-nilpotent provided that X is closed under taking subgroups and epimorphic images. If X is not closed under taking epimorphic images, we have to impose local p-solubility to G. In this case, the hypothesis of pronormality can be removed.

2010 Mathematics subject classification: 20E15, 20F19, 20F22

Keywords: locally finite group; hyperfinite group; p-nilpotency

Paper «On fixed points of the lower set operator» published in Internat. J. Algebra Comput.

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J. Almeida, A. Cano, O. Klíma, J.-É. Pin

On fixed points of the lower set operator

Internat. J. Algebra Comput., 25(1-2) (2015), 259–292

http://dx.doi.org/10.1142/S021819671540010X

Abstract

Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigroups, including all examples found in the literature. This is achieved by constructing six types of inequalities that are preserved by the lower set operator. These types of inequalities are shown to be independent in a certain sense. Several applications are also presented, including the preservation of the period for a pseudovariety of ordered semigroups whose image under the lower set operator is proper.Read More: http://www.worldscientific.com/doi/10.1142/S021819671540010X

2010 Mathematics subject classification: Primary: 20M07, Secondary: 20M35

Keywords: Ordered semigroups; pseudovarieties; lower sets; power operator; inequalities; pseudoidentities

Visita de Paz Jiménez Seral

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Paz Jiménez

La profesora Paz Jiménez Seral, del Departamento de Matemáticas de la Universidad de Zaragoza, visita la Universitat de València entre el miércoles 15 y el viernes 17 de abril de 2015. Paz es investigadora del proyecto «Propiedades aritméticas y estructurales de los grupos, aplicaciones II», coordinado con el nuestro, y trabaja en el estudio de los grupos finitos a través de sus acciones y en clases de grupos finitos.