342 名前:inciple, always work. In Case 1, take X=G/H. In Case 2, let H′=?g∈GgHg?1 be the normal core of H. It is easy to show that (since H has finite index), H′ is a finite index normal subgroup of G which is contained in H. Take X=G/H′ and f to be the quotient map. answered Oct 26 '09 at 16:15 Pete L. Clark