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

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 “A bound on the p-length of p-solvable groups” published in Glasg. Math. J.

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Jon González-Sánchez, Francesca Spagnuolo

A bound on the p-length of p-solvable groups

Glasg. Math. J., 57(1) (2015), 167–171

http://dx.doi.org/10.1017/S0017089514000196

Abstract

Let G be a finite p-solvable group and P a Sylow p-subgroup of G. Suppose that $\gamma_{\ell (p-1)}(P)\subseteq \gamma_r(P)^{p^s}$ for ℓ(p−1) < r + s(p − 1), then the p-length is bounded by a function depending on ℓ.

2010 Mathematics subject classification: primary 20D10; secondary 20D15