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February 2012 Finite p-groups which determine p-nilpotency locally
Thomas S. WEIGEL
Hokkaido Math. J. 41(1): 11-29 (February 2012). DOI: 10.14492/hokmj/1330351337


Let G be a finite group, and let p be a prime number. It might happen that the p-Sylow normalizer NG(P), P ∈ Sylp(G), of G is p-nilpotent, but G will not be p-nilpotent (see Example 1.1). However, under certain hypothesis on the structure of the Sylow p-subgroup P of G, this phenomenon cannot occur, e.g., by J. Tate's p-nilpotency criterion this is the case if P is a Swan group in the sense of H-W. Henn and S. Priddy. In this note we show that if P does not contain subgroups of a certain isomorphism type Yp(m) — in which case we call the p-group P slim — the previously mentioned phenomenon will not occur provided p is odd. For p = 2 the same remains true if P is D8-free (see Main Theorem).


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Thomas S. WEIGEL. "Finite p-groups which determine p-nilpotency locally." Hokkaido Math. J. 41 (1) 11 - 29, February 2012.


Published: February 2012
First available in Project Euclid: 27 February 2012

zbMATH: 1244.20018
MathSciNet: MR2920097
Digital Object Identifier: 10.14492/hokmj/1330351337

Primary: 20D20
Secondary: 20D15

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics


Vol.41 • No. 1 • February 2012
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