http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9978 We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller–Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognized by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata. 2012-06-25T23:37:31.238Z ]]>