2022/10/30 by Yuyama, Takao
#20F10 #68Q45 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2210.16879
Elder, Kambites, and Ostheimer showed that if the word problem of a finitely generated group H is accepted by a G-automaton for an abelian group G, then H is virtually abelian. We give a new, elementary, and purely combinatorial proof to the theorem. Furthermore, our method extracts an explicit connection between the two groups G and H from the automaton as a group homomorphism from a subgroup of G onto a finite index subgroup of H.