In this note we compute the equivariant Whiteheadgroups WHG(X) introduced by S. Illman. Because a G-homotopy equivalence is in general not isovariant, and a G-diffeomorphism is isovariant, the group WhG(X) does not give the right invariants for the equivariant s-cobordism theorem. So we introduce the isovariant Whiteheadgroup IWhG(X), prove an isovariant s-cobordism theorem and give some applications.
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