A filtration of spectra arising from families of subgroups of symmetric groups

Author:
Kathryn Lesh

Journal:
Trans. Amer. Math. Soc. **352** (2000), 3211-3237

MSC (2000):
Primary 55P47; Secondary 55N20, 55P42

DOI:
https://doi.org/10.1090/S0002-9947-00-02610-6

Published electronically:
March 15, 2000

MathSciNet review:
1707701

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Abstract: Let be a family of subgroups of which is closed under taking subgroups and conjugates. Such a family has a classifying space, , and we showed in an earlier paper that a compatible choice of for each gives a simplicial monoid , which group completes to an infinite loop space. In this paper we define a filtration of the associated spectrum whose filtration quotients, given an extra condition on the families, can be identified in terms of the classifying spaces of the families of subgroups that were chosen. This gives a way to go from group theoretic data about the families to homotopy theoretic information about the associated spectrum. We calculate two examples. The first is related to elementary abelian -groups, and the second gives a new expression for the desuspension of as a suspension spectrum.

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Additional Information

**Kathryn Lesh**

Affiliation:
Department of Mathematics, University of Toledo, Toledo, Ohio 43606-3390

Email:
klesh@uoft02.utoledo.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02610-6

Received by editor(s):
November 26, 1997

Published electronically:
March 15, 2000

Article copyright:
© Copyright 2000
American Mathematical Society