Two bounds for the nilpotence class of an algebra
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- by Benjamin Allen Otto PDF
- Proc. Amer. Math. Soc. 138 (2010), 1949-1953 Request permission
Abstract:
Supercharacters, which mimic the irreducible characters of certain $p$-groups, yield bounds on the nilpotence class of an algebra. Specifically, if an algebra $J$ has either $n$ superdegrees or $n$ superclass sizes, then $J^{n+1}=0$.References
- Persi Diaconis and I. M. Isaacs, Supercharacters and superclasses for algebra groups, Trans. Amer. Math. Soc. 360 (2008), no. 5, 2359–2392. MR 2373317, DOI 10.1090/S0002-9947-07-04365-6
- Thomas Michael Keller, Derived length and conjugacy class sizes, Adv. Math. 199 (2006), no. 1, 88–103. MR 2187399, DOI 10.1016/j.aim.2004.11.002
- A. Jaikin-Zapirain and Alexander Moretó, Character degrees and nilpotence class of finite $p$-groups: an approach via pro-$p$ groups, Trans. Amer. Math. Soc. 354 (2002), no. 10, 3907–3925. MR 1926859, DOI 10.1090/S0002-9947-02-02992-6
- Thomas Michael Keller, Derived length and conjugacy class sizes, Adv. Math. 199 (2006), no. 1, 88–103. MR 2187399, DOI 10.1016/j.aim.2004.11.002
Additional Information
- Benjamin Allen Otto
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
- Address at time of publication: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
- Email: botto@bgsu.edu
- Received by editor(s): July 14, 2009
- Received by editor(s) in revised form: September 21, 2009
- Published electronically: January 20, 2010
- Communicated by: Martin Lorenz
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1949-1953
- MSC (2010): Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-10-10229-9
- MathSciNet review: 2596028