General solution of the 2-cocycle functional equation on solvable groups
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- Ebanks, B. Aequ. math. (2007) 73: 260. doi:10.1007/s00010-006-2849-3
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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.