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Lifting wreath product extensions


Author: Elena V. Black
Journal: Proc. Amer. Math. Soc. 129 (2001), 1283-1288
MSC (2000): Primary 14H30, 14E20, 14D10; Secondary 12F10, 13B05
DOI: https://doi.org/10.1090/S0002-9939-00-05797-X
Published electronically: October 24, 2000
MathSciNet review: 1814179
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Abstract:

Let $G$ and $H$ be finite groups and let $K$ be a hilbertian field. We show that if $G$ has a generic extension over $K$ and $H$ satisfies the arithmetic lifting property over $K$, then the wreath product $G\wr H$ of $G$ and $H$ also satisfies the arithmetic lifting property over $K$. Moreover, if the orders of $H$ and $G$ are relatively prime and $G$ is abelian, then any extension of $G$ by $H$(which is necessarily a semidirect product) has the arithmetic lifting property.


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Additional Information

Elena V. Black
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: eblack@math.ou.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05797-X
Received by editor(s): August 9, 1999
Published electronically: October 24, 2000
Communicated by: Michael Stillman
Article copyright: © Copyright 2000 American Mathematical Society

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