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Group Rings of Dihedral Groups

  • F. E. A. JohnsonEmail author
Chapter
  • 950 Downloads
Part of the Algebra and Applications book series (AA, volume 17)

Abstract

In this chapter we continue the study of stably free cancellation over the integral group rings Z[F n ×Φ] in the case where Φ is the dihedral group of order 2m defined by the presentation
$$D_{2m} = \langle x, y \vert x^m = y^2 = 1 , yx = x^{m-1}y \rangle.$$
Our main result, first proved in Johnson (Q. J. Math., 2011, doi: 10.1093/qmath/har006), is that Z[F n ×D 2p ] has SFC when p is an odd prime. This breaks down for p=2. Although Z[C ×D 4] still has SFC (the case n=1) when n≥2 a result of O’Shea shows that Z[F n ×D 4] has infinitely many isomorphically distinct stably free modules of rank 1.

Keywords

Commutative Diagram Commutative Ring Group Ring Free Module Dihedral Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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