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$ p$-groups have unbounded realization multiplicity


Authors: Jen Berg and Andrew Schultz
Journal: Proc. Amer. Math. Soc. 142 (2014), 2281-2290
MSC (2010): Primary 12F10, 12F12
DOI: https://doi.org/10.1090/S0002-9939-2014-11967-8
Published electronically: March 11, 2014
MathSciNet review: 3195753
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Abstract: In this paper we interpret the solutions to a particular Galois embedding problem over an extension $ K/F$ satisfying $ \operatorname {Gal}(K/F) \simeq \mathbb{Z}/p^n\mathbb{Z}$ in terms of certain Galois submodules within the parameterizing space of elementary $ p$-abelian extensions of $ K$; here $ p$ is a prime. Combined with some basic facts about the module structure of this parameterizing space, this allows us to exhibit a class of $ p$-groups whose realization multiplicity is unbounded.


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Additional Information

Jen Berg
Affiliation: Department of Mathematics, University of Texas at Austin, One University Station C1200, Austin, Texas 78712-0257
Email: jberg@math.utexas.edu

Andrew Schultz
Affiliation: Department of Mathematics, Wellesley College, 106 Central Street, Wellesley, Massachusetts 02482
Email: andrew.c.schultz@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-11967-8
Received by editor(s): October 11, 2011
Received by editor(s) in revised form: June 30, 2012, and July 24, 2012
Published electronically: March 11, 2014
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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