Geodesic
A sufficient condition for reduction by stages: proof and applications
Sbornik. Mathematics, Tome 199 (2008) no. 5, pp. 663-671

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In this paper we prove the Marsden-Misiołek-Ortega-Perlmutter-Ratiu Stages Hypothesis, which is a sufficient condition for a general reduction by stages theorem. Our Lie-algebraic approach allows us to prove this conjecture in a general case (not only for semidirect products of groups with cocycle) and to simplify the proof of a general reduction by stages theorem (with some modifications). Bibliography: 8 titles. 
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     title = {A sufficient condition for reduction by stages: proof and applications},
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I. V. Mykytyuk; A. M. Stepin. A sufficient condition for reduction by stages: proof and applications. Sbornik. Mathematics, Tome 199 (2008) no. 5, pp. 663-671. http://geodesic.mathdoc.fr/item/SM_2008_199_5_a2/