Revista Matemática Iberoamericana

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Volume 20, Issue 2, 2004, pp. 413–425
DOI: 10.4171/RMI/395

Published online: 2004-08-31

On some permutable products of supersoluble groups

Manuel J. Alejandre[1], Adolfo Ballester-Bolinches[2], John Cossey[3] and Mari Carmen Pedraza-Aguilera[4]

(1) Universidad Miguel Hernández, Elche, Spain
(2) Universitat de València, Burjassot (Valencia), Spain
(3) Australian National University, Canberra, Australia
(4) Universidad Politecnia de Valencia, Spain

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.

Keywords: Finite groups, products, subnormality, supersolubility

Alejandre Manuel, Ballester-Bolinches Adolfo, Cossey John, Pedraza-Aguilera Mari Carmen: On some permutable products of supersoluble groups. Rev. Mat. Iberoam. 20 (2004), 413-425. doi: 10.4171/RMI/395