Understanding the Principle of Lifting Invariants in Lie Algebras

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I'm trying to read Serre's book on Lie algebras and have run into something I can't figure out. Luckily it's on google books so I'll just post a link to the point in question:

http://books.google.com/books?id=ha...&q="principle of lifting invariants"&f=false"

What the heck is the principle of lifting invariants? I can't find anything useful on google easily, and attempts to just prove the result myself fall short (I'm not even sure what the hypothesis is supposed to be, or what the principle is supposed to state exactly). Any illumination would be greatly appreciated
 
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Unfortunately it is hard to read, esp. whether and if so what ##s## is. Lifting in the context of exact sequences normally refers to a process of recovering something in opposite direction. Here we consider a preimage under the surjective transformation, and possibly whether it is already in the submodule.
 

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