Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Freyd’s generating hypothesis with almost split sequences
HTML articles powered by AMS MathViewer

by Jon F. Carlson, Sunil K. Chebolu and Ján Mináč PDF
Proc. Amer. Math. Soc. 137 (2009), 2575-2580 Request permission

Abstract:

Freyd’s generating hypothesis for the stable module category of a non-trivial finite group $G$ is the statement that a map between finitely generated $kG$-modules that belongs to the thick subcategory generated by the field $k$ factors through a projective module if the induced map on Tate cohomology is trivial. In this paper we show that Freyd’s generating hypothesis fails for $kG$ when the Sylow $p$-subgroup of $G$ has order at least $4$ using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd’s generating hypothesis for the stable module category of a finite group. We also derive some consequences of the generating hypothesis.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20C20, 20J06, 55P42
  • Retrieve articles in all journals with MSC (2000): 20C20, 20J06, 55P42
Additional Information
  • Jon F. Carlson
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 45415
  • Email: jfc@math.uga.edu
  • Sunil K. Chebolu
  • Affiliation: Department of Mathematics, Illinois State University, Normal, Illinois 61790
  • Email: schebol@ilstu.edu
  • Ján Mináč
  • Affiliation: Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
  • Email: minac@uwo.ca
  • Received by editor(s): June 12, 2008
  • Received by editor(s) in revised form: October 21, 2008
  • Published electronically: February 6, 2009
  • Additional Notes: The first author is partially supported by a grant from the NSF
    The third author is supported by the NSERC
  • Communicated by: Birge Huisgen-Zimmermann
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2575-2580
  • MSC (2000): Primary 20C20, 20J06; Secondary 55P42
  • DOI: https://doi.org/10.1090/S0002-9939-09-09826-8
  • MathSciNet review: 2497468