WoG 2024 Talk 2.6: Takao Yuyama - Groups Whose Word Problems Are Accepted by Abelian $G$-Automata

Speaker: Takao Yuyama
Institution: RIMS Kyoto

Title: Groups Whose Word Problems Are Accepted by Abelian $G$-Automata
Abstract: In 2008, Elder, Kambites, and Ostheimer showed that if a finitely generated group $H$ has a word problem accepted by a $G$-automaton for an abelian group $G$, then $H$ has an abelian subgroup of finite index. However, their proof relies on Gromov's theorem on groups of polynomial growth, despite the combinatorial setting. We give an elementary and combinatorial proof of the theorem, which does not involve any geometric arguments.

Видео WoG 2024 Talk 2.6: Takao Yuyama - Groups Whose Word Problems Are Accepted by Abelian $G$-Automata канала World of GroupCraft