Archivo de la etiqueta: Locally finite group

Paper “On locally finite groups whose subgroups of infinite rank have some permutable property” published in Ann. Mat. Pura Appl.

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A. Ballester-Bolinches, S. Camp-Mora, M. R. Dixon, R. Ialenti, and F. Spagnuolo

On locally finite groups whose subgroups of infinite rank have some permutable property

Ann. Mat. Pura Appl. (4), 196(5):1855–1862, 2017

https://doi.org/10.1007/s10231-017-0642-7

Abstract

In this paper, we study the behavior of locally finite groups of infinite rank whose proper subgroups of infinite rank have one of the three following properties, which are generalizations of permutability: S-permutability, semipermutability and S-semipermutability. In particular, it is proved that if G is a locally finite group of infinite rank whose proper subgroups of infinite rank are S-permutable (resp. semipermutable), then G is locally nilpotent (resp. all subgroups are semipermutable). For locally finite groups whose proper subgroups of infinite rank are S-semipermutable, the same statement can be proved only for groups with min-p for every prime p. A counterexample is given for the general case.

2010 Mathematical Subject Classification: 20F19, 20F50

Keywords: Locally finite group, Section p-rank, Section rank, Special rank, Permutable, Sylow permutable, Semipermutable, S-semipermutable

 

Defensa tesis doctoral Francesca Spagnuolo 21/02/2017 12.00

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Feb ’17
21
12:00

El próximo martes día 21 de febrero de 2017, a las 12.00, se procederá a la defensa de la tesis doctoral de Francesca Spagnuolo titulada «Some results on locally finite groups», dirigida por Adolfo Ballester Bolinches y Francesco de Giovanni, en el salón de grados de la Facultat de Matemàtiques de la Universitat de València.

Estáis todos invitados.

 

Paper “On groups whose subgroups of infinite rank are Sylow permutable” published in Ann. Mat. Pura Appl.

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

On groups whose subgroups of infinite rank are Sylow permutable.

Ann. Mat. Pura Appl. (4), 195(3):717–723, 2016.

https://doi.org/10.1007/s10231-015-0485-z

Abstract

In this paper, we investigate the structure of locally finite groups of infinite section rank (respectively, special rank) whose subgroups of infinite section rank (respectively, special rank) are Sylow permutable, permutable or normal. Some earlier results for locally finite groups appear as consequences of our study.

2010 Mathematics Subject Classification: 20E15, 20F19, 20F22

Keywords: Locally finite group, Section p-rank, Section rank, Special rank, Permutable, Sylow permutable, Normal

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 «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 «A note on Sylow permutable subgroups of infinite groups» published in J. Algebra

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

A note on Sylow permutable subgroups of infinite groups

J. Algebra, 398, 156-161 (2014)

http://dx.doi.org/10.1016/j.jalgebra.2013.08.042

Abstract: A subgroup A of a periodic group G is said to be Sylow permutable,
or S-permutable, subgroup of G if A P = P A for all Sylow subgroups
P of G. The aim of this paper is to establish the local nilpotency
of the section A^G /Core_G( A) for an S-permutable subgroup A of a
locally finite group G.
MSC: 20E15, 20F19, 20F22
Keywords: Locally finite group, Hyperfinite group, Sylow permutability, Ascendant subgroup

Paper «Groups with every subgroup ascendant-by-finite» published in Cent. Eur. J. Math.

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Sergio Camp-Mora

Groups with every subgroup ascendant-by-finite

Cent. Eur. J. Math., 11(12), 2182-2185 (2013)

http://dx.doi.org/10.2478/s11533-013-0312-y

Abstract: A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

MSC:  20F19, 20F22, 20F50
Keywords: Ascendant subgroup, Locally nilpotent, Radical, Locally finite 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