Geodesic
The Jordan-Hölder theorem and prefrattini subgroups of finite groups
Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 265-277

Voir la notice de l'article provenant de la source Cambridge University Press

All groups considered are finite. In recent years a number of generalizations of the classic Jordan-Hölder Theorem have been obtained (see [7], Theorem A.9.13): in a finite group G a one-to-one correspondence as in the Jordan-Holder Theorem can be defined preserving not only G-isomorphic chief factors but even their property of being Frattini or non-Frattini chief factors. In [2] and [13] a new direction of generalization is presented: the above correspondence can be defined in such a way that the corresponding non-Frattini chief factors have the same complement (supplement). 
Ballester-Bolinches, A.; Ezquerro, L. M. The Jordan-Hölder theorem and prefrattini subgroups of finite groups. Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 265-277. doi: 10.1017/S0017089500031554
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