Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T16:16:44.613Z Has data issue: false hasContentIssue false
  • English
  • Français

The Transfer in the Invariant Theory of Modular Permutation Representations II

Published online by Cambridge University Press:  20 November 2018

Mara D. Neusel
Mara D. Neusel*
Affiliation:
University of Notre Dame, Department of Mathematics, 370 CCMB, Notre Dame, Indiana 46556-5683, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we show that the image of the transfer for permutation representations of finite groups is generated by the transfers of special monomials. This leads to a description of the image of the transfer of the alternating groups. We also determine the height of these ideals.

Keywords

13A50polynomial invariants of finite groupspermutation representationtransfer
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 272 - 282
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Bertin, Marie-José, Anneau des Invariants du Groupe Alterné, en Caractéristic 2. Bull. Sci. Math. (2) 94 (1970), 94–1970.Google Scholar
[2] Campbell, H. E. A., Hughes, I. P., Shank, R. J. and Wehlau, D. L., Bases for Rings of Coinvariants. Transformation Groups 1 (1996), 1–1996.Google Scholar
[3] Feshbach, Mark, p-Subgroups of Compact Lie Groups and Torsion of Infinite Height in H*(BG, Fp). Michigan Math. J. 29 (1982), 29–1982.Google Scholar
[4] Göbel, Manfred, Computing Bases for Rings of Permutation-Invariant Polynomials. J. Symb. Comput. 19 (1995), 19–1995.Google Scholar
[5] Killius, Nelson, Göbel's Bound for Permutation Groups. unpublished notes, Evanston, 1995.Google Scholar
[6] Kuhnigk, Kathrin, Der Transfer in der modularen Invariantentheorie. Diplomarbeit, Göttingen, 1997.Google Scholar
[7] Kuhnigk, Kathrin and Smith, Larry, Feshbach's Transfer Theorem and Applications. AG Invariantentheorie, 1998, preprint.Google Scholar
[8] Neusel, Mara D., The Transfer in the Invariant Theory of Modular Permutation Representations. Pacific J. Math., to appear.Google Scholar
[9] Neusel, Mara D., A Selection from the 1001 Examples. The Atlas of the Invariant Theory of Finite Groups. in preparation.Google Scholar
[10] Neusel, Mara D. and Smith, Larry, Invariant Theory of Finite Groups. Encyclopaedia of Math., Springer-Verlag, Heidelberg, to appear.Google Scholar
[11] James Shank, R. and Wehlau, David L., The Transfer in Modular Invariant Theory. J. Pure Appl. Algebra 142 (1999), 142–1999.Google Scholar
[12] Smith, Larry, Polynomial Invariants of Finite Groups. Research Notes in Mathematics, A. K. Peters Ltd., Wellesley, Massachusetts, 2nd corrected printing, 1997.Google Scholar
[13] Smith, Larry, electronic communication. October 25, 1999.Google Scholar