The authors haracterize the finite groups in which H(G) , the intersection of the maximal non nilpotent subgroups of G , is nilpotent , but different from the Frattini subgroup. Further if F is a saturated foprmation and if F(G) is the intersection of all the maximal subgroups of G not belonging to F , a necessary and sufficient condition is given for F(G) to be nilpotent different from the Frattini subgroup .
Some results about a theorem of Shidov
GILOTTI, ANNA LUISA;
2006
Abstract
The authors haracterize the finite groups in which H(G) , the intersection of the maximal non nilpotent subgroups of G , is nilpotent , but different from the Frattini subgroup. Further if F is a saturated foprmation and if F(G) is the intersection of all the maximal subgroups of G not belonging to F , a necessary and sufficient condition is given for F(G) to be nilpotent different from the Frattini subgroup .File in questo prodotto:
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