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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Local subgroups and the stable category
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by Wayne W. Wheeler PDF
Trans. Amer. Math. Soc. 354 (2002), 2187-2205 Request permission

Abstract:

If $G$ is a finite group and $k$ is an algebraically closed field of characteristic $p>0$, then this paper uses the local subgroup structure of $G$ to define a category $\mathfrak {L}(G,k)$ that is equivalent to the stable category of all left $kG$-modules modulo projectives. A subcategory of $\mathfrak {L}(G,k)$ equivalent to the stable category of finitely generated $kG$-modules is also identified. The definition of $\mathfrak {L}(G,k)$ depends largely but not exclusively upon local data; one condition on the objects involves compatibility with respect to conjugations by arbitrary group elements rather than just elements of $p$-local subgroups.
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Additional Information
  • Wayne W. Wheeler
  • Affiliation: Center for Communications Research, 4320 Westerra Court, San Diego, California 92121
  • Email: wheeler@member.ams.org
  • Received by editor(s): January 2, 2001
  • Received by editor(s) in revised form: September 24, 2001
  • Published electronically: February 14, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2187-2205
  • MSC (2000): Primary 20C20
  • DOI: https://doi.org/10.1090/S0002-9947-02-02964-1
  • MathSciNet review: 1885649