Abstract
Letp be a prime,G a periodic solvablep′-group acted on by an elementary groupV of orderp 2. We show that ifC G(v) is abelian for eachv ∈V # thenG has nilpotent derived group, and ifp=2 andC G(v) is nilpotent for eachv ∈V # thenG is metanilpotent. Earlier results of this kind were known only for finite groups.
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Shumyatsky, P. On periodic solvable groups having automorphisms with nilpotent fixed point groups. Israel J. Math. 87, 111–116 (1994). https://doi.org/10.1007/BF02772987
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DOI: https://doi.org/10.1007/BF02772987