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Journal of Algebra
We study languages of geodesics in lamplighter groups and Thompson's group F. We show that the lamplighter groups L_n have infinitely many cone types, have no regular geodesic languages, and have 1-counter, context-free and counter geodesic languages with respect to certain generating sets. We show that the full language of geodesics with respect to one generating set for the lamplighter group is not counter but is context-free, while with respect to another generating set the full language ofdoi:10.1016/j.jalgebra.2005.11.016 fatcat:ujmtwxghord3ngj5svqtxx4ebq