On the existence of equivariant embeddings of principal bundles into vector bundles. Proc. Amer. Math. Soc. 88 (1983), no. 1, 157–161. Suppose that X has homotopy type of a k-dimensional connected CW-complex, k ≥ 1 and let p: V → X be an m-dimensional G-vector bundle in which the finite group G acts effectively on each fiber of p. Let n be the minimum of the codimensions of the fixed-point sets of the restriction of the elements of G to the fibers of p. The authors show that if 1 ≤ k < n then any principal G-bundle over X can be embedded equivariantly into V. In particular, if the action of G is free outside of the zero section for p, then any principal G-bundle over X can be embedded equivariantly int
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