Some Hopf Galois structures arising from elementary abelian $p$-groups
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- by Lindsay N. Childs PDF
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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 $s = \frac {(m-1)^2}3 - m$.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3453-3460
- MSC (2000): Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9939-07-08888-0
- MathSciNet review: 2336557