General solution of the 2-cocycle functional equation on solvable groups
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The general solution of the 2-cocycle functional equation on abelian groups is well known. Methods are also known for finding regular solutions on Lie groups. Here we find general solutions of the 2-cocycle equation on certain non-abelian groups. We consider groups that are semidirect products, and in particular solvable groups that can be built up by splitting extensions.
Mathematics Subject Classification (2000).Primary 39B52 Secondary 20C35
Keywords.Solvable group semidirect product splitting extension normal subgroup 2-cocycle cocycle
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