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MR686148 (84b:57035) 57S17 (55Q70 57S25)
Petrie, Ted The equivariant $J$ homomorphism and Smith equivalence of representations. Current trends in algebraic topology, Part 2 (London, Ont., 1981), pp. 223–233, CMS Conf. Proc., 2, Amer. Math. Soc., Providence, R.I., 1982.
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