Charla “Teoría del endomorfismo, recurrencias lineales y ecuaciones diferenciales”, Ramón Esteban Romero, jueves 19/04/2018, 13.00

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Dijous 19/04/2018, a les 13.00, a la sala «Charles Darwin» del campus de Burjassot (Facultat de Farmàcia) impartiré la xarrada amb títol «Teoria de l’endomorfisme, recurrències lineals i equacions diferencials», dins del cicle de conferències dels seminaris de les assignatures de segon i tercer del grau de Matemàtiques.

Esteu tots convidats.

El jueves 19/04/2018, a las 13.00, en la sala «Charles Darwin» del campus de Burjassot (Facultat de Farmàcia) impartiré la charla titulada «Teoría del endomorfismo, recurrencias lineales y ecuaciones diferenciales», dentro del ciclo de conferencias de los seminarios de las asignaturas de segundo y tercero del grado de Matemáticas.

Estáis todos invitados.

Paper “On two questions from the Kourovka Notebook” published in J. Algebra

The following paper has been published:

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A. Ballester-Bolinches, John Cossey, S. F. Kamornikov, H. Meng.

On two questions from the Kourovka Notebook

J. Algebra, 499:438-449, 2018

https://doi.org/10.1016/j.jalgebra.2017.12.014

Abstract

The aim of this paper is to give answers to some questions concerning intersections of system normalisers and prefrattini subgroups of finite soluble groups raised by the third author, Shemetkov and Vasil’ev in the Kourovka Notebook [10]. Our approach depends on results on regular orbits and it can be also used to extend a result of Mann [9] concerning intersections of injectors associated to Fitting classes.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite groups. Soluble groups. Formations. Fitting classes. Prefrattini  subgroups. Normalisers. Injectors.

Paper “On two classes of finite supersoluble groups” published in Comm. Algebra

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W. M. Fakieh, R. A. Hijazi, A. Ballester-Bolinches, J. C. Beidleman

On two classes of finite supersoluble groups

Comm. Algebra., 46 (3):1110-1115, 2018

doi:10.22108/ijgt.2017.21214

Abstract

Let Z be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called Z-S-semipermutable if H permutes with every Sylow p-subgroup of G in Z for all p not in π(H); H is said to be Z-S-seminormal if it is normalized by every Sylow p-subgroup of G in Z for all p not in π(H). The main aim of this paper is to characterize the Z-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in Z are Z-S-semipermutable in G and the Z-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in Z are Z-S-seminormal in G.

2010 Mathematics Subject Classification: 20D10; 20D20; 20D35; 20D40

Keywords: Finite group; permutability; soluble group; supersoluble group; Sylow sets

Paper “On a theorem of Kang and Liu on factorised groups” published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, M. C. Pedraza Aguilera

On a theorem of Kang and Liu on factorised groups

Bull. Austral. Math. Soc., 97 (1):54-56, 2018

https://doi.org/10.1017/S0004972717000363

Abstract

Kang and Liu [‘On supersolvability of factorized finite groups’, Bull. Math. Sci. 3 (2013), 205–210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is to give a correct proof of their main theorem.

2010 Mathematics Subject Classification: primary: 20D10, secondary: 20D20, 20D40

Keywords: finite group. factorisation, supersolubility

Paper “Prime Power Indices in Factorised Groups” published in Mediterr. J. Math.

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Prime power indices in factorised groups.

Mediterr. J. Math., 14(6):Art. 225, 15, 2017

https://doi.org/10.1007/s00605-016-0987-9

Abstract

Let the group G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in AB have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in AB have prime power indices in G. In particular, when G=A=B, we obtain as a consequence some known results.

2010 Mathematics Subject Classification: 20D10, 20D40, 20E45, 20D20

Keywords: Finite groups, Products of groups, Conjugacy classes, Sylow subgroups

Paper “Square-free class sizes in products of groups” published in J. Algebra

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Square-free class sizes in products of groups

J. Algebra, 491:190–206, 2017

https://doi.org/10.1016/j.jalgebra.2017.08.007

Abstract

We obtain some structural properties of a factorised group G=AB, given that the conjugacy class sizes of certain elements in AB are not divisible by , for some prime p. The case when G=AB is a mutually permutable product is especially considered.

2010 Mathematical Subject Classification: 20D10, 20D40, 20E45

Keywords: Finite groups, Soluble groups, Products of subgroups, Conjugacy classes

 

Paper “On complements of F-residuals of finite groups” published in Comm. Algebra

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A. Ballester-Bolinches, S. F. Kamornikov, and V. Pérez-Calabuig

On Complements of F-residuals of finite groups

Comm. Algebra, 45(2):878–882, 2017.

https://doi.org/10.1080/00927872.2016.1175615

Abstract

A formation F of finite groups has the generalized Wielandt property for residuals, or is a GWP-formation, if the F-residual of a group generated by two F-subnormal subgroups is the subgroup generated by their F-residuals. The main aim of the paper is to determine some sufficient conditions for a finite group to split over its F-residual.

2010 Mathematics subject classification: 20D10; 20D20

Keywords: Finite group; formation; residual; subnormality

Paper “Normalisers of residuals of finite groups” published in Arch. Math. (Basel)

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A. Ballester-Bolinches, S. F. Kamornikov, and H. Meng

Normalisers of residuals of finite groups

Arch. Math. (Basel), 109(4):305–310, 2017

https://doi.org/10.1007/s00013-017-1074-8

Abstract:

Let F be a subgroup-closed saturated formation of finite groups containing all finite nilpotent groups, and let M be a subgroup of a finite group G normalising the F-residual of every non-subnormal subgroup of G. We show that M normalises the F-residual of every subgroup of G. This answers a question posed by Gong and Isaacs (Arch Math 108:1–7, 2017) when F is the formation of all finite supersoluble groups.

2010 Mathematics Subject Classification: 20D10, 20D35

Keywords: Finite group, Formation, Residual, Subnormality

Paper “Finite groups with all minimal subgroups solitary” published in J. Algebra Appl.

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R. Esteban-Romero and Orieta Liriano.

Finite groups with all minimal subgroups solitary.

J. Algebra Appl., 15(8):1650140, 9, 2016

https://doi.org/10.1142/S0219498816501401

Abstract 

We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order.

2010 Mathematical Subject Classification: 20D10, 20D30

Keywords: Finite group; solitary subgroup; minimal subgroup

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