Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



$ 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
Published electronically: March 11, 2014
MathSciNet review: 3195753
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 12F10, 12F12

Retrieve articles in all journals with MSC (2010): 12F10, 12F12

Additional Information

Jen Berg
Affiliation: Department of Mathematics, University of Texas at Austin, One University Station C1200, Austin, Texas 78712-0257

Andrew Schultz
Affiliation: Department of Mathematics, Wellesley College, 106 Central Street, Wellesley, Massachusetts 02482

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.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia