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On automorphisms of free pro-$ p$-groups. I


Authors: Wolfgang N. Herfort and Luis Ribes
Journal: Proc. Amer. Math. Soc. 108 (1990), 287-295
MSC: Primary 20E18; Secondary 20E36
DOI: https://doi.org/10.1090/S0002-9939-1990-0984794-6
MathSciNet review: 984794
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Abstract: Let $ F$ be a (topologically) finitely generated free pro-$ p$-group, and $ \beta $ an automorphism of $ F$. If $ p \ne 2$ and the order of $ \beta $ is 2, then there is some basis of $ F$ such that $ \beta $ either fixes or inverts its elements. If $ p$ does not divide the order of $ \beta $, then the subgroup of $ F$ of all elements fixed by $ \beta $ is (topologically) infinitely generated; however this is not always the case if $ p$ divides the order of $ \beta $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0984794-6
Article copyright: © Copyright 1990 American Mathematical Society

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