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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Stably splitting BG
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by Dave Benson PDF
Bull. Amer. Math. Soc. 33 (1996), 189-198 Request permission


In the early nineteen eighties, Gunnar Carlsson proved the Segal conjecture on the stable cohomotopy of the classifying space $BG$ of a finite group $G$. This led to an algebraic description of the ring of stable self-maps of $BG$ as a suitable completion of the “double Burnside ring”. The problem of understanding the primitive idempotent decompositions of the identity in this ring is equivalent to understanding the stable splittings of $BG$ into indecomposable spectra. This paper is a survey of the developments of the last ten to fifteen years in this subject.
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Additional Information
  • Dave Benson
  • Affiliation: Department of Mathematics, University of Georgia, Athens GA 30602, USA
  • MR Author ID: 34795
  • Email:
  • Additional Notes: Partly supported by a grant from the NSF
  • © Copyright 1996 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 33 (1996), 189-198
  • MSC (1991): Primary 55P
  • DOI:
  • MathSciNet review: 1362628