Geodesic
The Influence on a Finite Group of its Permutable Subgroups
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 159-165

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

Huppert, Janko and Mann have proved the following theorems for a finite group G.(Huppert [4]). If each second maximal subgroup of G is normal in G, then G is supersolvable. If the order of G is divisible by at least three different primes, then G is nilpotent.(Huppert [4]). Let each third maximal subgroup of G be normal in G. Then: (i) G′ is nilpotent; (ii) the rank of G=r(G)≤2; (iii) if |G| is divisible by at least three different primes, then G is supersolvable. 
Agrawal, Ram K. The Influence on a Finite Group of its Permutable Subgroups. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 159-165. doi: 10.4153/CMB-1974-033-4
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