# Conferencia Arnold D. Feldman 16/04/2019

 Abr ’19 16 12:00

El próximo martes 16 de abril a las 12.00h en el Seminario del IUMPA (UPV) el profesor Arnold Feldman, del Franklin & Marshall College (Lancaster, PA, EEUU), impartirá una conferencia titulada «Analogues of pronormality in $\sigma$-solvable finite groups». Estáis todos invitados.

Abstract
This is a preliminary talk about topics in finite groups that I am discussing with M.D. Pérez-Ramos and Rex Dark. Skiba and others have studied a generalization of solvability that they call σ-solvability, where σ is a partition of the set of prime integers. When σ is the partition in which each set contains exactly one prime, σ-solvability is just solvability. Many properties of solvable groups and their subgroups have analogues in σ-solvable groups. In this talk, we introduce two possible generalizations of pronormality, which we call σ-pronormality and weak σ-pronormality, and describe how they interact with other subgroup properties, including σ-subnormality as defined in Skiba’s work.

# Visitas de Rex Dark y Arnold D. Feldman (30/03-30/04/2019)

 Mar ’19 Abr 30 30

Los profesores Rex Dark (National University of Ireland, Galway, Irlanda) y Arnold D. Feldman (Franklin and Marshall College, Lancaster, PA, Estados Unidos de América) nos visitan del 30 de marzo al 30 de abril de 2019.  Ambos son especialistas en teoría abstracta de grupos finitos, en particular, en clases de grupos y permutabilidad y colaboradores habituales del equipo de investigación.

# Paper «On generalised pronormal subgroups of finite groups» published in Glasgow Math. J.

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

A. Ballester-Bolinches, J. C. Beidleman, A. D. Feldman, M. F. Ragland

On generalised pronormal subgroups of finite groups

Glasgow Math. J., 56(3) (2014), 691–703

http://dx.doi.org/10.1017/S0017089514000159

Abstract

For a formation , a subgroup M of a finite group G is said to be -pronormal in G if for each g ∈ G, there exists x ∈ 〈U,Ug such that Ux = Ug . Let f be a subgroup embedding functor such that f(G) contains the set of normal subgroups of G and is contained in the set of Sylow-permutable subgroups of G for every finite group G. Given such an f, let fT denote the class of finite groups in which f(G) is the set of subnormal subgroups of G; this is the class of all finite groups G in which to be in f(G) is a transitive relation in G. A subgroup M of a finite group G is said to be -normal in G if G/Core G(M) belongs to . A subgroup U of a finite group G is called K--subnormal in G if either U = G or there exist subgroups U = U 0U 1 ≤ . . . ≤ Un = G such that Ui–1 is either normal or -normal in Ui , for i = 1,2, …, n. We call a finite group G an -group if every K--subnormal subgroup of G is in f(G). In this paper, we analyse for certain formations the structure of -groups. We pay special attention to the -pronormal subgroups in this analysis.

2010 Mathematics subject classification: 20D10; 20D35; 20F17

# Paper «Finite solvable groups in which semi-normality is a transitive relation» published in Beitr. Algebra Geom.

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

A. Ballester-Bolinches, J. C. Beidleman, A. D. Feldman, H. Heineken, M. F. Ragland

Finite solvable groups in which semi-normality is a transitive relation

Beitr. Algebra Geom., 54(2), 549-558 (2013)

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

Abstract: A subgroup H of a finite group G is said to be seminormal in G if every Sylow p-subgroup of G, p a prime, with (|H|, p) = 1 normalizes H. A group G is called an SNT-group if seminormality is a transitive relation in G. Properties of solvable SNT-groups are studied. For example, subgroups of solvable SNT-groups are SNT-groups.
MSC: 20D05, 20D10, 20F16
Keywords: Finite groups, S-permutability, S-semipermutability, seminormal.

# Paper «On generalised subnormal subgroups of finite groups» published in Math. Nachr.

The paper

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

has appeared in Mathematische Nachrichten, 286, No. 11-12, 1066-1171 (2013). It is available through

http://dx.doi.org/10.1002/mana.201200029

See abstract below.

El artículo

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

ha aparecido en Mathematische Nachrichten, 286, No. 11-12, 1066-1171 (2013). Ya está accesible a través de

http://dx.doi.org/10.1002/mana.201200029

Véase el resumen al final.

L’article

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

ha aparegut en Mathematische Nachrichten, 286, No. 11-12, 1066-1171 (2013). Està accessible per mitjà de

http://dx.doi.org/10.1002/mana.201200029

Al final se’n pot veure el resum.

Abstract:

Let F be a formation of finite groups. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. A subgroup U of a finite group G is called a K-F-subnormal subgroup of G if either U = G or there exist subgroups U = U0U1 ≤ … ≤ Un = G such that Ui − 1 is either normal or F-normal in Ui, for i = 1, 2, …, n. The K-F-subnormality could be regarded as the natural extension of the subnormality to formation theory and plays an important role in the structural study of finite groups. The main purpose of this paper is to analyse classes of finite groups whose K-F-subnormal subgroups are exactly the subnormal ones. Some interesting extensions of well-known classes of groups emerge.

Keywords: Formation; F-subnormal Subgroup; Subnormal Subgroup; PST-groups; PT-groups; T-groups

MSC (2010): 20D10; 20D35; 20F17

https://permut.blogs.uv.es/2013/04/02/paper-on-generalised-subnormal-subgroups-of-finite-groups/

# Paper «On generalised subnormal subgroups of finite groups» to appear in Math. Nachr.

The paper

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

will be published in Mathematische Nachrichten. It is available through

http://dx.doi.org/10.1002/mana.201200029

We will inform about the final publication details. See abstract below.

El artículo

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

será publicado en Mathematische Nachrichten. Ya está accesible a través de

http://dx.doi.org/10.1002/mana.201200029

Informaremos sobre los detalles bibliográficos cuando estén disponibles. Véase el resumen al final.

L’article

A. Ballester-Bolinches, James Beidleman, A. D. Feldman, M. F. Ragland,

On generalised subnormal subgroups of finite groups

serà publicat en Mathematische Nachrichten. Ja està accessible per mitjà de

http://dx.doi.org/10.1002/mana.201200029

Informarem sobre els detalls bibliogràfics quan estiguen disponibles. Al final es pot veure el resum.

Abstract:

Let be a formation of finite groups. A subgroup M of a finite group G is said to be -normal in G if G/CoreG(M) belongs to . A subgroup U of a finite group G is called a K--subnormal subgroup of G if either U = G or there exist subgroups U = U0U1 ≤ … ≤ Un = G such that Ui − 1 is either normal or -normal in Ui, for i = 1, 2, …, n. The K--subnormality could be regarded as the natural extension of the subnormality to formation theory and plays an important role in the structural study of finite groups. The main purpose of this paper is to analyse classes of finite groups whose K--subnormal subgroups are exactly the subnormal ones. Some interesting extensions of well-known classes of groups emerge.

Keywords: Formation; -subnormal Subgroup; Subnormal Subgroup; PST-groups; PT-groups; T-groups

MSC (2010): 20D10; 20D35; 20F17