If G is a non soluble finite group the intersection of the maximal subgroups of G that are not nilpotent is the Frattini subgroup of G. This was proved by Shidov (1971). The authors present a new formation larger than the formation of nilpotent groups for which it holds the analogous of the theorem of Shidov. The theorem uses the classification of finite simple groups.
A.L.Gilotti, U.Tiberio (2009). On the "Shidov property" and a formation satisfying it. COMMUNICATIONS IN ALGEBRA, 37, 1-11 [10.1080/00927870802278883].
On the "Shidov property" and a formation satisfying it
GILOTTI, ANNA LUISA;
2009
Abstract
If G is a non soluble finite group the intersection of the maximal subgroups of G that are not nilpotent is the Frattini subgroup of G. This was proved by Shidov (1971). The authors present a new formation larger than the formation of nilpotent groups for which it holds the analogous of the theorem of Shidov. The theorem uses the classification of finite simple groups.File in questo prodotto:
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