Cohomology, fusion and a p-nilpotency criterion

Details Cohomology, fusion and a p-nilpotency criterion Cohomology, fusion and a p-nilpotency criterion

2009-04-16

arxiv.org/abs/0904.2503v2

Mathematics

Group Theory

7 pages

Scientific paper

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, 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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