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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sets of integers as superdegrees and superclass sizes


Author: Benjamin Allen Otto
Journal: Proc. Amer. Math. Soc. 139 (2011), 1309-1319
MSC (2010): Primary 20C15
Published electronically: October 29, 2010
MathSciNet review: 2748424
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Abstract: Supercharacters have recently been proposed as a sort of stand-in for the characters of $ p$-groups. If $ q>1$ is a prime power, then every set of $ q$-powers that contains $ 1$ is both a set of superdegrees and a set of superclass sizes. Moreover, if $ r$ and $ s$ are integers that are greater than $ 1$, then there is an algebra with exactly $ r$ superdegrees and exactly $ s$ superclass sizes. These results are direct analogs of results from the theory of $ p$-groups.


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Additional Information

Benjamin Allen Otto
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: botto@bgsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10748-7
PII: S 0002-9939(2010)10748-7
Received by editor(s): May 1, 2010
Published electronically: October 29, 2010
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.