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=⊔ σ∈G/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).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Campbell, H.E.A.E., Wehlau, D.L. (2011). The Transfer. In: Modular Invariant Theory. Encyclopaedia of Mathematical Sciences, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17404-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-17404-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17403-2
Online ISBN: 978-3-642-17404-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)