Geodesic
A Characteristic Subgroup of a p-Stable Group
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1101-1135

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

Let p be a prime, and let S be a Sylow p-subgroup of a finite group G. J. Thompson (13; 14) has introduced a characteristic subgroup JR(S) and has proved the following results:(1.1) Suppose that p is odd. Then G has a normal p-complement if and only if C(Z(S)) and N(JR(S)) have normal p-complements. 
Glauberman, George. A Characteristic Subgroup of a p-Stable Group. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1101-1135. doi: 10.4153/CJM-1968-107-2
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