Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 10 (2015), 2303-2324.
The abelian monoid of fusion-stable finite sets is free
We show that the abelian monoid of isomorphism classes of -stable finite -sets is free for a finite group with Sylow -subgroup ; here a finite -set is called -stable if it has isomorphic restrictions to -conjugate subgroups of . These -stable -sets are of interest, e.g., in homotopy theory. We prove freeness by constructing an explicit (but somewhat nonobvious) basis, whose elements are in one-to-one correspondence with the -conjugacy classes of subgroups in . As a central tool of independent interest, we give a detailed description of the embedding of the Burnside ring for a saturated fusion system into its associated ghost ring.
Algebra Number Theory, Volume 9, Number 10 (2015), 2303-2324.
Received: 3 December 2014
Revised: 31 August 2015
Accepted: 8 October 2015
First available in Project Euclid: 16 November 2017
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Reeh, Sune. The abelian monoid of fusion-stable finite sets is free. Algebra Number Theory 9 (2015), no. 10, 2303--2324. doi:10.2140/ant.2015.9.2303. https://projecteuclid.org/euclid.ant/1510842447