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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Two bounds for the nilpotence class of an algebra

Author(s): Benjamin Allen Otto
Journal: Proc. Amer. Math. Soc. 138 (2010), 1949-1953.
MSC (2010): Primary 20C15
Posted: January 20, 2010
MathSciNet review: 2596028
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Abstract | References | Similar articles | Additional information

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:

1.
Persi Diaconis and I. M. Isaacs, Supercharacters and superclasses for algebra groups. Transactions of the American Mathematical Society 360 (2008), 2359-2392. MR 2373317 (2009c:20012)

2.
I. M. Isaacs and D. S. Passman, Derived length and conjugacy class sizes, Advances in Mathematics 199 (2006), 88-103. MR 2187399 (2006k:20027)

3.
A. Jaikin-Zapirain and Alexander Moretó, Character degrees and nilpotence class of finite $ p$-groups: An approach via pro-$ p$ groups, Transactions of the American Mathematical Society 354 (2002), 3907-3925. MR 1926859 (2003m:20005)

4.
Thomas Michael Keller, Derived length and conjugacy class sizes, Advances in Mathematics 199 (2006), 88-103. MR 2187399 (2006k:20027)

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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

DOI: 10.1090/S0002-9939-10-10229-9
PII: S 0002-9939(10)10229-9
Received by editor(s): July 14, 2009,
Received by editor(s) in revised form: September 21, 2009
Posted: January 20, 2010
Communicated by: Martin Lorenz
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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