The nilpotence height of

Authors:
G. Walker and R. M. W. Wood

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1291-1295

MSC (1991):
Primary 55S10

DOI:
https://doi.org/10.1090/S0002-9939-96-03203-0

MathSciNet review:
1307571

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A 20-year-old conjecture about the mod 2 Steenrod algebra , namely that the element has nilpotence height , is proved. The proof uses formulae of D. M. Davis and J. H. Silverman to obtain commutation relations involving `atomic' and the canonical antiautomorphism of , together with a `stripping' technique for obtaining new relations in from old. This construction goes back to Kristensen [Math. Scand. 16 (1965), 97--115].

**1.**J. F. Adams, letter to D. M. Davis, February 1985.**2.**D. Arnon, Monomial bases in the Steenrod algebra, J. Pure Appl. Algebra**96**(1994), 215--223. CMP**95:04****3.**D. P. Carlisle and R. M. W. Wood, On an ideal conjecture in the Steenrod algebra, preprint 1994. (Former title: Facts and fancies about relations in the Steenrod algebra.)**4.**D. M. Davis, The antiautomorphism of the Steenrod algebra, Proc. Amer. Math. Soc. 44 (1974), 235--236. MR**48:7276****5.**D. M. Davis, On the height of , preprint 1985.**6.**V. Giambalvo and F. Peterson, On the height of , preprint, MIT 1994.**7.**L. Kristensen, On a Cartan formula for secondary cohomology operations, Math. Scand. 16 (1965), 97--115. MR**33:4926****8.**K. G. Monks, Nilpotence in the Steenrod algebra, Bol. Soc. Mat. Mexicana**37**(1992), 401--416.**9.**K. G. Monks, Status report: On the height of , Preprint, Univ. of Scranton, Pennsylvania, 1991.**10.**K. G. Monks, The nilpotence height of , Proc. Amer. Math. Soc.**124**(1996), 1297--1303.**11.**J. Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150--171. MR**20:6092****12.**J. H. Silverman, Conjugation and excess in the Steenrod algebra, Proc. Amer. Math. Soc. 119 (1993), 657--661. MR**93k:55020****13.**P. D. Straffin, Jr., Identities for conjugation in the Steenrod algebra, Proc. Amer. Math. Soc. 49 (1975), 253--255. MR**52:1693****14.**R. M. W. Wood, A note on bases and relations in the Steenrod algebra, preprint 1993, Bull. London Math. Soc.**27**(1995), 380--386.

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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