Abstract
The authors characterize the finite groups in which \(\,\mathcal{H} (G)\), the intersection of the maximal non-nilpotent subgroups of G, is nilpotent, but different from Φ(G). Further, if \(\,\mathcal{F} \,\) is a saturated formation and if \(\,\mathcal{F}(G)\,\) is the intersection of all maximal subgroups of G not belonging to \(\,\mathcal{F}\), a necessary and sufficient condition is given for \(\,\mathcal{F}(G)\,\) to be nilpotent different from Φ(G).
Keywords: Frattini subgroup, Maximal subgroups, Saturated formation
Mathematics Subject Classification (2000): 20B05, 20D10, 20D25,20E28
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gilotti, A.L., Tiberio, U. Some results about a theorem of Shidov. Ann. Univ. Ferrara 52, 99–106 (2006). https://doi.org/10.1007/s11565-006-0009-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11565-006-0009-2