Paper “Groups whose primary subgroups are normal sensitive” published in Monatsh. Math.

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Adolfo Ballester-Bolinches, Leonid A. Kurdachenko, Javier Otal, and Tatiana Pedraza

Groups whose primary subgroups are normal sensitive

Monatsh. Math., 175(2) (2014), 175–185

http://dx.doi.org/10.1007/s00605-013-0566-2

Abstract

A subgroup H of a group G is said to be normal sensitive in G if for every normal subgroup N of H,N=H∩NG. In this paper we study locally finite groups whose p-subgroups are normal sensitive. We show the connection between these groups and groups in which Sylow permutability is transitive.

2010 Mathematics subject classification: 20E07; 20E15; 20F22; 20F50

Keywords: Locally finite group; Normal sensitivity; Primary subgroup; PST-group; T-group

Paper “Groups whose primary subgroups are normal sensitive” to appear in Monatsh. Math.

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Adolfo Ballester-Bolinches, Leonid A. Kurdachenko, Javier Otal, Tatiana Pedraza

Groups whose primary subgroups are normal sensitive

Monats. Math.

http://dx.doi.org/10.1007/s00605-013-0566-2

Abstract: A subgroup H of a group G is said to be normal sensitive in G if for every normal subgroup N of H, N = H ∩ N^G . In this paper we study locally finite groups whose p-subgroups are normal sensitive. We show the connection between these groups and groups in which Sylow permutability is transitive.

Keywords: Locally finite group, Normal sensitivity, Primary subgroup, PST-group, T-group

Mathematics Subject Classification (2000):  20E07, 20E15, 20F22, 20F50

Paper “Extension of Schur theorem to groups with a central factor with a bounded section rank” published in J. Algebra

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A. Ballester-Bolinches, S. Camp-Mora, L. A. Kurdachenko, J. Otal

Extension of Schur theorem to groups with a central factor with a bounded section rank

J. Algebra, 393, 1-15 (2013)

http://dx.doi.org/10.1016/j.jalgebra.2013.06.035

Abstract: A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.

MSC: 20F14, 20F19, 20F99

Keywords: Schur class, Schur multiplier, Special rank of a group, p-section rank of a group, 0-rank of a group, Generalized radical group