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If      F →  E →  B F \to E \to B       is a fibration with      F = K ( G , 1 ) F = K(G,1)      ,      G G       Abelian, and      B = K ( ∏  , 1 ) B = K(\prod ,1)      , then it is shown that the action and characteristic class of the fibration correspond to those of the induced group extension.

On characteristic classes of groups and bundles of $K(\Pi ,\,1)$’s