Permutable products of supersoluble groups

Manuel J. Alejandre; Adolfo Ballester-Bolinches; John Cossey

doi:10.1016/j.jalgebra.2003.01.002

Permutable products of supersoluble groups

Manuel J. Alejandre, Adolfo Ballester-Bolinches^*, John Cossey

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.

Original language	English
Pages (from-to)	453-461
Number of pages	9
Journal	Journal of Algebra
Volume	276
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2003.01.002
Publication status	Published - 15 Jun 2004

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10.1016/j.jalgebra.2003.01.002

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title = "Permutable products of supersoluble groups",

abstract = "We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.",

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AU - Alejandre, Manuel J.

AU - Ballester-Bolinches, Adolfo

AU - Cossey, John

PY - 2004/6/15

Y1 - 2004/6/15

N2 - We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.

AB - We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.

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U2 - 10.1016/j.jalgebra.2003.01.002

DO - 10.1016/j.jalgebra.2003.01.002

M3 - Article

SN - 0021-8693

VL - 276

SP - 453

EP - 461

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Permutable products of supersoluble groups

Abstract

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