Paper “A Note on Solitary Subgroups of Finite Groups” published in Comm. Algebra

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R. Esteban-Romero and Orieta Liriano

A note on solitary subgroups of finite groups.

Comm. Algebra, 44(7):2945–2952, 2016

https://doi.org/10.1080/00927872.2015.1065855

Abstract

We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups.

2010 Mathematics Subject Classification: 20D10, 20D30, 20F16

Keywords: Finite group, Fitting class, Formation, Quotient solitary subgroup, Solitary subgroup

Paper “On S-Semipermutable Subgroups and Soluble PST-Groups” published in Mediterr. J. Math.

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

On S-semipermutable subgroups and soluble PST-groups

Mediterr. J. Math., 14(2):Art. 87, 6, 2017

https://doi.org/10.1007/s00009-017-0893-y

Abstract

All groups presented in this article are finite. Using several permutability embedding properties, a number of new characterisations of soluble PST-groups are studied.

2010 Mathematics subject classification:  20D10; 20D20; 20F16

Keywords: Finite group; Permutability; S-Semipermutability

 

Paper “On finite groups with many supersoluble subgroups” published in Arch. Math. (Basel)

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A. Ballester-Bolinches, R. Esteban-Romero, and Jiakuan Lu

On finite groups with many supersoluble subgroups

Arch. Math. (Basel), 109(1):3–8, 2017

https://doi.org/10.1007/s00013-017-1041-4

Abstract

The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A_5 or SL_2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A_5 or SL_2(5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201–206, 2012).

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, Supersoluble subgroup, Soluble group

 

Paper “On subgroup functors of finite soluble groups” published in Sci. China Math.

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Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Sergey Fedorovich Kamornikov

On subgroup functors of finite soluble groups.

Sci. China Math., 60(3):439–448, 2017

https://doi.org/10.1007/s11425-015-0330-9

Abstract

The principal aim of this paper is to study the regular and transitive subgroup functors in the universe of all finite soluble groups. We prove that they form a complemented and non-modular lattice containing two relevant sublattices. This is the answer to a question (Question 1.2.12) proposed by Skiba (1997) in the finite soluble universe.

2010 Mathematics subject classification: 20D10; 20D30

Keywords: finite group; soluble group; lattices of subgroups; subgroup functors; formations

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 “2-Engel relations between subgroups” published in J. Algebra

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M. P. Gállego, P. Hauck, and M. D. Pérez-Ramos

2-Engel relations between subgroups

J. Algebra, 447:31–55, 2016

https://doi.org/10.1016/j.jalgebra.2015.08.030

Abstract

In this paper we study groups G generated by two subgroups A and B such that 〈a, bis nilpotent of class at most 2 for all aA and  bB . A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups.

2010 Mathematical Subject Classification: Primary 20F45; Secondary 20F18, 20D15, 20F12

Keywords: 2-Engel condition, 2-generated subgroups, L-connection, Nilpotency class

Paper “On the supersoluble hypercentre of a finite group” published in Monatsh. Math.

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Liyun Miao, Adolfo Ballester-Bolinches, Ramón Esteban-Romero, and Yangming Li

On the supersoluble hypercentre of a finite group

Monatsh. Math., 184(4):641–648, 2017

https://doi.org/10.1515/forum-2016-0262

Abstract

A subgroup H of a group G is called Sylow permutable, or S-permutable, in G if H permutes with all Sylow p-subgroups of G for all primes p. A group G is said to be a PST-group if Sylow permutability is a transitive relation in G. We show that a group G which is factorised by a normal subgroup and a subnormal PST-subgroup of odd order is supersoluble. As a consequence, the normal closure S^G of a subnormal PST-subgroup S of odd order of a group G is supersoluble, and the subgroup generated by subnormal PST-subgroups of G of odd order is supersoluble as well.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, p-Supersoluble group, S-semipermutable subgroup

Paper “On the focal subgroup of a saturated fusion system” published in J. Algebra

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, Ning Su, and Yanming Wang.

On the focal subgroup of a saturated fusion system.

J. Algebra, 468:72–79, 2016

https://doi.org/10.1016/j.jalgebra.2016.07.034

Abstract

The influence of the cyclic subgroups of order p or 4 of the focal subgroup of a saturated fusion system F over a p-group S is investigated in this paper. Some criteria for normality of S in F as well as necessary and sufficient conditions for nilpotency of F are given. The resistance of a p-group in which every cyclic subgroup of order p or 4 is normal, and earlier results about p-nilpotence of finite groups and nilpotency of saturated fusion systems are consequences of our study.

2010 Mathematical Subject Classification: 20C20

Keywords: Saturated fusion system, Control of fusion

Paper “On hall subnormally embedded subgroups of finite groups” published in Monatsh. Math.

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Adolfo Ballester-Bolinches, John Cossey, and ShouHong Qiao.

On Hall subnormally embedded subgroups of finite groups.

Monatsh. Math., 181(4):753–760, 2016

https://doi.org/10.1007/s00605-015-0838-0

Abstract

A subgroup H of a finite group G is said to be Hall subnormally (respectively normally) embedded in G if there is a subnormal (respectively normal) subgroup N of G such that H is a Hall subgroup of N. The aim of this paper is to characterise the groups G having a Hall subnormally embedded subgroup of order |B| for each subgroup B of G. Some earlier results are consequences of our main theorem.

2010 Mathematical Subject Classification: 20D10 20D20

Keywords: Finite group, Soluble group, Hall subgroup, Subnormal subgroup

Paper “On the exponent of mutually permutable products of two abelian groups” published in J. Algebra

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A. Ballester-Bolinches, John Cossey, and M. C. Pedraza-Aguilera.

On the exponent of mutually permutable products of two abelian groups.

J. Algebra, 466:34–43, 2016.

https://doi.org/10.1016/j.jalgebra.2016.05.027

Abstract

In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian groups, and they are used to derive some interesting structural properties of such products.

2010 Mathematical Subject Classification: 20D10, 20D20

Keywords: Finite group, Abelian group, Exponent, Factorisations, p-Supersolubility, p-Length