On some permutable products of supersoluble groups

Manuel J. Alejandre; A. Ballester-Bolinches; John Cossey; M. C. Pedraza-Aguilera

doi:10.4171/RMI/395

On some permutable products of supersoluble groups

Manuel J. Alejandre^*
, A. Ballester-Bolinches
, John Cossey
, M. C. Pedraza-Aguilera

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.

Original language	English
Pages (from-to)	413-425
Number of pages	13
Journal	Revista Matematica Iberoamericana
Volume	20
Issue number	2
DOIs	https://doi.org/10.4171/RMI/395
Publication status	Published - 2004

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title = "On some permutable products of supersoluble groups",

abstract = "It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.",

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AU - Alejandre, Manuel J.

AU - Ballester-Bolinches, A.

AU - Cossey, John

AU - Pedraza-Aguilera, M. C.

PY - 2004

Y1 - 2004

N2 - It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.

AB - It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.

KW - Finite groups

KW - Products

KW - Subnormality

KW - Supersolubility

UR - https://www.scopus.com/pages/publications/4043133720

U2 - 10.4171/RMI/395

DO - 10.4171/RMI/395

M3 - Article

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VL - 20

SP - 413

EP - 425

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 2

ER -

On some permutable products of supersoluble groups

Abstract

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