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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$p$-groups have unbounded realization multiplicity
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by Jen Berg and Andrew Schultz PDF
Proc. Amer. Math. Soc. 142 (2014), 2281-2290 Request permission

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
  • MR Author ID: 1061301
  • 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
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 3195753