## $p$-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.## References

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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