Elementary abelian operator groups |
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Authors: | Pavel Shumyatsky |
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Institution: | (1) Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel |
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Abstract: | Letp be a prime,n a positive integer. Suppose thatG is a finite solvablep'-group acted on by an elementary abelianp-groupA. We prove that ifC
G
(ϕ) is of nilpotent length at mostn for every nontrivial element ϕ ofA and |A|≥p
n+1
thenG is of nilpotent length at mostn+1. |
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Keywords: | |
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