, Volume 73, Issue 3, pp 260-279

General solution of the 2-cocycle functional equation on solvable groups

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Summary.

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.

Manuscript received: August 19, 2005 and, in final form, July 10, 2006.