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The nilpotence height of $Sq^{2^n}$


Authors: G. Walker and R. M. W. Wood
Journal: Proc. Amer. Math. Soc. 124 (1996), 1291-1295
MSC (1991): Primary 55S10
MathSciNet review: 1307571
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Abstract: A 20-year-old conjecture about the mod 2 Steenrod algebra $A$, namely that the element $Sq^{2^n}$ has nilpotence height $2n+2$, is proved. The proof uses formulae of D. M. Davis and J. H. Silverman to obtain commutation relations involving `atomic' $Sq^i$ and the canonical antiautomorphism of $A$, together with a `stripping' technique for obtaining new relations in $A$ from old. This construction goes back to Kristensen [Math. Scand. 16 (1965), 97--115].


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Additional Information

G. Walker
Affiliation: Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom
Email: grant@ma.man.ac.uk

R. M. W. Wood
Affiliation: Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom
Email: reg@ma.man.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-96-03203-0
Received by editor(s): June 16, 1992
Received by editor(s) in revised form: October 7, 1994
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society