Geodesic
An Extension of a Theorem of Janko on Finite Groups with Nilpotent Maximal Subgroups
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 550-552

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

Throughout this paper G will denote a finite group containing a nilpotent maximal subgroup S and P will denote the Sylow 2-subgroup of S. The largest subgroup of S normal in G will be designated by core (S) and the largest solvable normal subgroup of G by rad(G). All other notation is standard.Thompson [6] has shown that if P = 1 then G is solvable. Janko [3] then observed that G is solvable if P is abelian, a condition subsequently weakened by him [4] to the assumption that the class of P is ≦ 2 . Our purpose is to demonstrate the sufficiency of a still weaker assumption about P. 
Randolph, John W. An Extension of a Theorem of Janko on Finite Groups with Nilpotent Maximal Subgroups. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 550-552. doi: 10.4153/CJM-1971-060-3
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[1] 1. Alperin, J., Sylow intersections and fusion, J. Algebra 6 (1967), 222–241. Google Scholar

[2] 2. Feit, W., Characters of finite groups (Benjamin, New York, 1967). Google Scholar

[3] 3. Janko, Z., Verallgemeinerung eines satzes von B. Huppert una J. G. Thompson, Arch. Math. 12 (1961), 280–281. Google Scholar

[4] 4. Janko, Z., Finite groups with a nilpotent maximal subgroup, J. Austral. Math. Soc. 4 (1964), 449–451. Google Scholar

[5] 5. Randolph, J., Finite groups with solvable maximal subgroups, Proc. Amer. Math. Soc. 23 (1969), 490–492. Google Scholar

[6] 6. Thompson, J., Normal p-complements for finite groups, Math. Z. 72 (1960), 332–354. Google Scholar

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