On some permutable products of supersoluble groups
Alejandre, Manuel J. ; Ballester-Bolinches, A. ; Cossey, John ; Pedraza-Aguilera, M. C.
Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 413-425 / Harvested from Project Euclid
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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.
Publié le : 2004-06-14
Classification:  finite groups,  products,  subnormality,  supersolubility,  20D10,  20D35,  20D40 
@article{1087482021,
     author = {Alejandre, Manuel J. and Ballester-Bolinches, A. and Cossey, John and Pedraza-Aguilera, M. C.},
     title = {On some permutable products of supersoluble groups},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 413-425},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087482021}
}

Alejandre, Manuel J.; Ballester-Bolinches, A.; Cossey, John; Pedraza-Aguilera, M. C. On some permutable products of supersoluble groups. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  413-425. http://gdmltest.u-ga.fr/item/1087482021/