The object of this article is to show that a Jordan-Hölder class structure of a finite group determines abelian Hall subgroups of the group up to isomorphism. The proof uses this classification of the finite simple groups.
@article{urn:eudml:doc:41745, title = {The determination of abelian Hall subgroups by a conjugacy class structure.}, journal = {Publicacions Matem\`atiques}, volume = {36}, year = {1992}, pages = {685-691}, mrnumber = {MR1209833}, zbl = {0827.20025}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41745} }
Kimmerle, Wolfgang; Sandling, Robert. The determination of abelian Hall subgroups by a conjugacy class structure.. Publicacions Matemàtiques, Tome 36 (1992) pp. 685-691. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41745/