A p-nilpotency criterion |
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| Authors: | Jon Gonz��lez-S��nchez |
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| Institution: | 1. Departamento de Matem??ticas, Estad??stica y Computaci??n, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s/n, 39071, Santander, Spain
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| Abstract: | Let G be a finite group, p a fixed prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, then G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4. |
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