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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some Hopf Galois structures arising from elementary abelian $ p$-groups


Author: Lindsay N. Childs
Journal: Proc. Amer. Math. Soc. 135 (2007), 3453-3460
MSC (2000): Primary 16W30
DOI: https://doi.org/10.1090/S0002-9939-07-08888-0
Published electronically: June 22, 2007
MathSciNet review: 2336557
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Abstract: Let $ p$ be an odd prime, $ G = Z_p^m$, the elementary abelian $ p$-group of rank $ m$, and let $ \Gamma$ be the group of principal units of the ring $ \mathbb{F}_p[x]/(x^{m+1})$. If $ L/K$ is a Galois extension with Galois group $ \Gamma$, then we show that for $ p \ge 5$, the number of Hopf Galois structures on $ L/K$ afforded by $ K$-Hopf algebras with associated group $ G$ is greater than $ p^s$, where $ s = \frac {(m-1)^2}3 - m$.


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Additional Information

Lindsay N. Childs
Affiliation: Department of Mathematics and Statistics, University at Albany, Albany, New York 12222
Email: childs@math.albany.edu

DOI: https://doi.org/10.1090/S0002-9939-07-08888-0
Received by editor(s): February 13, 2006
Received by editor(s) in revised form: August 11, 2006
Published electronically: June 22, 2007
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.