Groups generated by 3-state automata over a 2-letter alphabet, I

Bondarenko, Ievgen; Grigorchuk, Rostislav; Kravchenko, Rostyslav; Muntyan, Yevgen; Nekrashevych, Volodymyr; Savchuk, Dmytro; Sunic, Zoran

Groups generated by 3-state automata over a 2-letter alphabet, I

Authors

Bondarenko, Ievgen

Grigorchuk, Rostislav

Kravchenko, Rostyslav

Muntyan, Yevgen

Nekrashevych, Volodymyr

Savchuk, Dmytro

Sunic, Zoran

Description

An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite, abelian, and free groups are classified. In addition, we provide detailed information and complete proofs for several groups from the class, with the intention of showing the main methods and techniques used in the classification.
37 pages, 52 figures