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

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

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

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

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 “A note on finite groups with the maximal permutiser condition” published in Rev. R. Acad. Cienc. Exactas Fí s. Nat. Ser. A Math. RACSAM

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

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

A note on finite groups with the maximal permutiser condition.

Rev. R. Acad. Cienc. Exactas Fí s. Nat. Ser. A Math. RACSAM, 110(1):247–250, 2016

https://doi.org/10.1007/s13398-015-0232-8

Abstract

A finite group G is said to satisfy the maximal permutiser condition, or G is an MPC-group, if for any maximal subgroup M of G, there is an element xGM such that G=Mx⟩. In this note, we show that the class of MPC-groups is not residually closed and so it is not a formation. It answers a question posed in Qiao et al. (J Algebra Appl 12(5):1250217, 2013). Following Ballester-Bolinches and Esteban-Romero (Commun Algebra 30(12):5757–5770, 2002), a finite group G is said to be a QP-group if G is soluble and if F is a non-cyclic chief factor of G, then F has order 4 and G induces the full automorphism group in F. We prove that the class of all QP-groups is the unique largest formation contained in the class of all MPC-groups. A detailed description of the MPC-groups is also given.

2010 Mathematics Subject Classification: 20D10, 20D15

Keywords: Finite group, Soluble group, Permutability, Formations

Paper “On a problem posed by S. Li and J. Liu” published in Arch. Math.

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

Adolfo Ballester-Bolinches, Shouhong Qiao

On a problem posed by S. Li and J. Liu

Arch. Math., 102, 109-111 (2014)

http://dx.doi.org/10.1007/s00013-014-0617-5

Abstract: A subgroup H of a finite group G is said to be Hall normally
embedded in G if there is a normal subgroup N of G such that H is a
Hall subgroup of N . The aim of this note is to prove that a group G has
a Hall normally embedded subgroup of order |B| for each subgroup B of
G if and only if G is soluble with nilpotent residual cyclic of square-free
order. This is the answer to a problem posed by Li and Liu (J. Algebra
388:1–9, 2013).


MSC: 20D10, 20D20
Keywords: Finite group, soluble group, Hall subgroups

Paper “On a paper posed by S. Li and J. Liu” to appear in Arch. Math.

The following paper has been accepted for publication.

El siguiente artículo ha sido aceptado para su publicación.

El següent article ha sigut acceptat per ser publicat.

Adolfo Ballester-Bolinches, Shouhong Qiao

On a problem posed by S. Li and J. Liu

Arch. Math., in press

http://dx.doi.org/10.1007/s00013-014-0617-5

Abstract: A subgroup H of a finite group G is said to be Hall normally
embedded in G if there is a normal subgroup N of G such that H is a
Hall subgroup of N . The aim of this note is to prove that a group G has
a Hall normally embedded subgroup of order |B| for each subgroup B of
G if and only if G is soluble with nilpotent residual cyclic of square-free
order. This is the answer to a problem posed by Li and Liu (J. Algebra
388:1–9, 2013).


MSC: 20D10, 20D20
Keywords: Finite group, soluble group, Hall subgroups

 

Charla Francesco de Giovanni

Abr ’13
12
12:00

DeGiovanniEl profesor Francesco de Giovanni, de la Università degli Studi di Napoli «Federico II», que nos visita entre el 9 y el 13 de abril de 2013, impartirá la charla titulada

Soluble groups of infinite rank

el próximo viernes día 12 de abril, a las 12.00, en el seminario del Departament d’Àlgebra de la Universitat de València (Facultat de Matemàtiques, 2º piso).

Estáis todos invitados.