Paper «On a theorem of Kang and Liu on factorised groups» published in Bull. Austral. Math. Soc.

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A. Ballester-Bolinches, M. C. Pedraza Aguilera

On a theorem of Kang and Liu on factorised groups

Bull. Austral. Math. Soc., 97 (1):54-56, 2018

https://doi.org/10.1017/S0004972717000363

Abstract

Kang and Liu [‘On supersolvability of factorized finite groups’, Bull. Math. Sci. 3 (2013), 205–210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is to give a correct proof of their main theorem.

2010 Mathematics Subject Classification: primary: 20D10, secondary: 20D20, 20D40

Keywords: finite group. factorisation, supersolubility

Publication data for «Maximal subgroups and PST-groups» in Cent. Eur. Math. J.

Central European Journal of MathematicsWe now have the issue and page numbers for the paper we mentioned in http://permut.blogs.uv.es/2013/03/15/paper-maximal-subgroups-and-pst-groups/.

Adolfo Ballester-Bolinches, James C. Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig

Maximal subgroups and PST-groups

Centr. Eur. J. Math., 11(6), 2013, 1078-1082,

available on http://dx.doi.org/10.2478/s11533-013-0222-z.

Abstract:

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

MSC:  20D05, 20D10, 20E15, 20E28, 20F16
Keywords: Finite groups • Permutability • Sylow-permutability • Maximal subgroups • Supersolubility

(c) Versita Sp. z. o. o. and Springer

 

Paper «Maximal subgroups and PST-groups» to appear in Cent. Eur. Math. J.

Central European Journal of MathematicsThe paper

Adolfo Ballester-Bolinches, James C. Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig

Maximal subgroups and PST-groups

Centr. Eur. J. Math., in press

is now available on http://dx.doi.org/10.2478/s11533-013-0222-z.

Abstract:

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

MSC:  20D05, 20D10, 20E15, 20E28, 20F16
Keywords: Finite groups • Permutability • Sylow-permutability • Maximal subgroups • Supersolubility

(c) Versita Sp. z. o. o. and Springer

We will inform about the volume and issue this paper is officially published.