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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Supported by the Spanish Ministry of Science, grant MTM2008-06680-C02-01.
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González-Sánchez, J. A p-nilpotency criterion. Arch. Math. 94, 201–205 (2010). https://doi.org/10.1007/s00013-009-0092-6
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DOI: https://doi.org/10.1007/s00013-009-0092-6