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The $p$-exponent of the $K(1)_*$-local spectrum $\Phi SU(n)$

Author: Michael J. Fisher
Journal: Proc. Amer. Math. Soc. 131 (2003), 3617-3621
MSC (2000): Primary 55P42
Published electronically: February 26, 2003
MathSciNet review: 1991776
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Abstract: Let $p$ be a fixed odd prime. In this paper we prove an exponent conjecture of Bousfield, namely that the $p$-exponent of the spectrum $\Phi SU(n)$is $(n-1) + \nu_p((n-1)!)$ for $n \geq 2$. It follows from this result that the $p$-exponent of $\Omega^{q} SU(n) \langle i \rangle$ is at least $(n-1) + \nu_p((n-1)!)$ for $n \geq 2$ and $i,q \geq 0$, where $SU(n) \langle i \rangle$ denotes the $i$-connected cover of $SU(n)$.

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Additional Information

Michael J. Fisher
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Address at time of publication: Department of Mathematics, California State University, Fresno, 5245 North Backer Avenue M/S PB 108, Fresno, California 93740

Received by editor(s): October 29, 2001
Received by editor(s) in revised form: June 7, 2002
Published electronically: February 26, 2003
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society