| May ’21 |
| 28 |
| 15:50 |
Vicent Pérez-Calabuig will give the talk «On the computability of the abelian kernel of an inverse semigroup» at 2021 Zassenhaus Groups and Friends Conference, online, on 28/05/2021 at 15.50. More information:
https://www2.math.binghamton.edu/p/zassenhaus/zassenhaus_2021/home
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
Adolfo Ballester-Bolinches, Vicent Pérez-Calabuig.
The abelian kernel of an inverse semigroup.
Mathematics, 8(8):1219 (12 pages), 2020.
Abstract
The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.
2020 Mathematics Subject Classification: 20M10, 20M17
Keywords: finite semigroup; abelian kernels; profinite topologies; partial automorphisms; extension problem
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
A. Ballester-Bolinches, S. F. Kamornikov, M. C. Pedraza-Aguilera, and V. Pérez-Calabuig.
On σ-subnormality criteria in finite σ-soluble groups.
Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 114(2):Paper No. 94, 9, 2020.
Abstract
Let σ = {σi : i ∈ I} be a partition of the set ℙ of all prime numbers. A subgroup X of a finite group G is called σ-subnormal in G if there is a chain of subgroups X = X0 ⊆ X1 ⊆⋯⊆ Xn = G where for every j=1,…,n the subgroup Xj-1 is normal in Xj or Xj/CoreXj(Xj-1) is a σi-group for some i ∈ I. In the special case that σ is the partition of ℙ into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. In this paper some σ-subnormality criteria for subgroups of σ-soluble groups, or groups in which every chief factor is a σi-group, for some i ∈ I, are showed.
2020 Mathematics Subject Classification: 20D10, 20D20
Keywords: finite group; σ-solubility; σ-nilpotency; σ-subnormal subgroup; factorised group
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
Adolfo Ballester-Bolinches and Vicent Pérez-Calabuig
An elementary proof of a theorem of Graham on finite semigroups.
Mathematics, 8(1):105 (5 pages), 2020.
Abstract
The purpose of this note is to give a very elementary proof of a theorem of Graham that provides a structural description of finite 0-simple semigroups and its idempotent-generated subsemigroups.
2010 Mathematics Subject Classification: 20M10, 20M17
Keywords: finite semigroup; regular semigroup; 0-simple semigroup
| Dic ’18 |
| 18 |
| 12:30 |
El proper dimarts 18 de desembre de 2018, 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 Vicent Pérez Calabuig amb títol «A reduction theorem for the generalised Rhodes’ Type II Conjecture» dirigida per Adolfo Ballester Bolinches.
Esteu tots convidats.
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
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.
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Vicente Pérez-Calabuig
A note on the rational canonical form of an endomorphism of a vector space of finite dimension
Operators and Matrices, 12 (3):823-836, 2018
Abstract
In this note, we give an easy algorithm to construct the rational canonical form of a square matrix or an endomorphism h of a finite dimensional vector space which does not depend on either the structure theorem for finitely generated modules over principal ideal domains or matrices over the polynomial ring. The algorithm is based on the construction of an element whose minimum polynomial coincides with the minimum polynomial of the endomorphism and on the fact that the h-invariant subspace generated by such an element admits an h-invariant complement. It is also shown that this element can be easily obtained without the factorisation of a polynomial as a product of irreducible polynomials.
2010 Mathematics Subject Classification: 15A21, 12E05, 12Y05
Keywords: Similarity of matrices, rational canonical form, minimum polynomial, endomorphism.
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
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
The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
A. Ballester-Bolinches, J. C. Beidleman, V. Pérez-Calabuig, and M. F. Ragland
On seminormal subgroups of finite groups
Rocky Mountain J. Math., 47(2):419–427, 2017
https://doi.org/10.1216/RMJ-2017-47-2-419
Abstract
All groups considered in this paper are finite. A subgroup H of a group G is said to be seminormal in G if H is normalized by all subgroups K of G such that gcd(|H|,|K|)=1 . We call a group G an MSN-group if the maximal subgroups of all the Sylow subgroups of G are seminormal in G. In this paper, we classify all MSN-groups.
2010 Mathematics Subject Classification: 20D10, 20D15, 20D20
Keywords: Finite group, soluble PST-group,T₀-group, MS-group, MSN-group
The following book chapter has been published:
El siguiente capítulo de libro ha sido publicado:
El capítol de llibre següent ha sigut publicat:
A. Ballester-Bolinches, V. Pérez-Calabuig.
On kernels of finite semigroups.
Overlapping of mathematics and humanities, 221-239, Quad. Mat., 20, Aracne, Rome, 2017.
ISBN 978-88-255-0237-4
Abstract:
A reduction theorem for the computability of the kernel of a finite semigroup associated to a variety of finite groups is presented in this survey article. This result turns out to be crucial in the proof of the computability of the prosoluble closure of a finitely generated subgroup of a free group.
2020 Mathematics Subject Classification: 20-02, 20M07.