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The Transfer

  • H. E. A. Eddy CampbellEmail author
  • David L. Wehlau
Chapter
  • 1.2k Downloads
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 139)

Abstract

In this chapter, we consider in detail the transfer (also called the trace) map introduced in §1.2. Let H be a subgroup of the finite group G. Choose a set of left coset representatives for H in G. We denote this set of representatives by G/H. Thus G=⊔ σG/H σH is a decomposition of G into left cosets. There is an extensive theory considering the relative versions of the results of this chapter, see Fleischmann (1999) or Fleischmann and Shank (2003).

Keywords

Normal Subgroup Prime Ideal Principal Ideal Coset Representative Left Coset 
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References

  1. 38.
    Peter Fleischmann, Relative trace ideals and Cohen-Macaulay quotients of modular invariant rings, Computational methods for representations of groups and algebras (Essen, 1997), Progr. Math., vol. 173, Birkhäuser, Basel, 1999, pp. 211–233. MR 1714612 (2000j:13007) Google Scholar
  2. 41.
    Peter Fleischmann and R. James Shank, The relative trace ideal and the depth of modular rings of invariants, Arch. Math. (Basel) 80 (2003), no. 4, 347–353. MR 2004e:13012 zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Sir Howard Douglas Hall, Dept. MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Dept. Mathematics & Computer ScienceRoyal Military College of CanadaKingstonCanada

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