# Defensa tesi doctoral Hangyang Meng 01/07/2019 12.30

 Jul ’19 1 12:30

El proper dilluns 1 de juliol de 2019, a les 12.30, a la sala de graus «Manuel Valdivia» de la Facultat de Ciències Matemàtiques de la Universitat de València es durà a terme la defensa de la tesi doctoral de Hangyang Meng amb títol

Regular orbits of actions of finite soluble groups. Applications

Esteu tots convidats.

# Paper «On products of generalised supersoluble finite groups» published in Mediterr. J. Math.

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A. Ballester-Bolinches, J. Cossey, H. Meng, M. C. Pedraza-Aguilera.
On products of generalised supersoluble finite groups
Ann. Mat. Pura Appl. (4), 198(3):811–819, 2019.

doi:10.1007/s10231-018-0800-6

Abstract

In this paper, mutually sn-permutable subgroups of groups belonging to a class of generalised supersoluble groups are studied. Some analogs of known theorems on mutually sn-permutable products are established.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, supersoluble group, Sn-permutability, factorisation

# Paper «On mutually permutable products of finite groups» published in Rend. Lincei. Mat. Appl.

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Adolfo Ballester-Bolinches, Yangming Li, Mari Carmen Pedraza-Aguilera.

On mutually permutable products of finite groups

Rend. Lincei. Mat. Appl., 29 (4):711-719, 2018

doi:10.4171/RLM/830

Abstract

The main purpose of this paper is to study mutually permutable products G=AB in which the subgroups of prime order p and cyclic of order 4 (if p=2) of the largest normal subgroup of G contained in A \cap B are well situated in G. Our results confirm once again the important role of the intersection of the factors in the structural study of mutually permutable products.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group, Sylow permutability, weakly s-supplementation, factorisation, saturated formation.

# Paper «On formations of finite groups with the generalized Wielandt property for residuals II» published in J. Algebra Appl.

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

On formations of finite groups with the generalized Wielandt property for residuals II

J. Algebra Appl., 17 (9):1850167 (8 pages), 2018

http://dx.doi.org/10.1142/S0219498818501670

Abstract

A formation F of finite groups has the generalized Wielandt property for residuals, or F 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 result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.

2010 Mathematics Subject Classification: 20D10, 20D20

Keywords: Finite group; formation; residual; subnormality.

# Paper «A note on normal complements for finite groups» published in Bull. Austral. Math. Soc.

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Ning Su, Adolfo Ballester-Bolinches, Hangyang Meng.

A note on normal complements for finite groups

Bull. Austral. Math. Soc., 98 (1):109-112, 2018

doi:10.1017/S0004972718000151

Abstract

Assume that G is a finite group and H is a 2-nilpotent Sylow tower Hall subgroup of G such that if x and y are G-conjugate elements of H ∩ G0 of prime order or order 4, then x and y are H-conjugate. We prove hat there exists a normal subgroup N of G such that G = HN and H ∩ N = 1.

2010 Mathematics Subject Classification: primary 20D20; secondary 20D10

Keywords: finite group, conjugation, Hall subgroup, normal complement.

# Paper «On metacyclic subgroups of finite groups» published in Internat. J. Group Th.

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A. Ballester-Bolinches

On metacyclic subgroups of finite groups

Internat. J. Group Theory, 7(2):25-29, 2018

http://dx.doi.org/10.22108/ijgt.2017.21480

Abstract

The aim of this survey article is to present some structural results about of groups whose Sylow p-subgroups are metacylic (p a prime). A complete characterisation of non-nilpotent groups whose 2-generator subgroups are metacyclic is also presented.

2010 Mathematics Subject Classification: Primary: 20D20; Secondary: 20E25.

Keywords: finite group, Sylow subgroups, metacyclic groups, 2-generator groups.

# Paper «On finite groups with square-free conjugacy class sizes» published in Int. J. Group Theory

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María José Felipe, Ana Martínez-Pastor, Víctor-Manuel Ortiz-Sotomayor

On finite groups with square-free conjugacy class sizes

Int. J. Group Th., 7 (2):17-24, 2018

doi:10.22108/ijgt.2017.21475

Abstract

We report on finite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.

2010 Mathematics Subject Classification: Primary: 20E45. Secondary: 20D40, 20D10, 20D20

Keywords: finite group, conjugacy class, factorised group

# Paper «Finite trifactorised groups and $\pi$-decomposability» published in Bull. Austral. Math. Soc.

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L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos.

Finite trifactorised groups and $\pi$-decomposability

Bull. Austral. Math. Soc., 97 (2):218-228, 2018

doi:10.1017/S0004972717001034

Abstract

We derive some structural properties of a trifactorised finite group G = AB = AC = BC, where A, B, and C are subgroups of G, provided that A = Aπ × Aπ’ and B = Bπ × Bπ’ are π-decomposable groups, for a set of primes π.

2010 Mathematics Subject Classification: primary 20D40; secondary 20D20

Keywords: finite group, product of subgroups, π-decomposable group, π-structure.

# 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