Archivo por meses: marzo 2016

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

Posted on por

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 x∈G∖M such that G=M⟨x⟩. 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 “Some Characterisations of Soluble SST-Groups” published in Comm. Algebra

Posted on por

The following paper has been published

El siguiente artículo ha sido publicado

El següent article ha sigut publicat

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

Some characterisations of soluble SST-groups.

Comm. Algebra, 44(4):1821–1827, 2016.

https://doi.org/10.1080/00927872.2015.1027397

Abstract

All groups considered in this paper are finite. A subgroup H of a group G is said to be SS-permutable or SS-quasinormal in G if H has a supplement K in G such that H permutes with every Sylow subgroup of K. Following [6 Chen, X. Y., Guo, W. B. (2014). Finite groups in which SS-permutability is a transitive relation. Acta Math. Hungar. 143(2):466–479.], we call a group G an SST-group provided that SS-permutability is a transitive relation in G, that is, if A is an SS-permutable subgroup of B and B is an SS-permutable subgroup of G, then A is an SS-permutable subgroup of G. The main aim of this paper is to present several characterisations of soluble SST-groups.

2010 Mathematics Subject Classification: Primary 20D10; Secondary 20D15, 20D20

Keywords: BT-group, Finite group, Soluble PST-group, SST-group