On some permutable products of supersoluble groups

Manuel J. Alejandre; Adolfo Ballester-Bolinches; John Cossey; Mari Carmen Pedraza-Aguilera

doi:10.4171/rmi/395

JournalsrmiVol. 20, No. 2pp. 413–425

On some permutable products of supersoluble groups

Manuel J. Alejandre
Universidad Miguel Hernández, Elche, Spain
Adolfo Ballester-Bolinches
Universitat de València, Burjassot (Valencia), Spain
John Cossey
Australian National University, Canberra, Australia
Mari Carmen Pedraza-Aguilera
Universidad Politecnia de Valencia, Spain

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Abstract

It is well known that a group $G = A B$ 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 $A N$ and $BN$ are supersoluble. We then exploit this to establish some sufficient conditions for $G$ to be supersoluble.

Cite this article

Manuel J. Alejandre, Adolfo Ballester-Bolinches, John Cossey, Mari Carmen Pedraza-Aguilera, On some permutable products of supersoluble groups. Rev. Mat. Iberoam. 20 (2004), no. 2, pp. 413–425

DOI 10.4171/RMI/395