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- W151915566 abstract "Given a group G and a positive integer d≥2 we introduce the notion of an automaton rank of a group G with respect to its self-similar actions on a d-ary tree of words as the minimal number of states in an automaton over a d-letter alphabet which generates this group (topologically if G is closed). We construct minimal automata generating free abelian groups of finite ranks, which completely determines automaton ranks of free abelian groups. We also provide naturally defined 3-state automaton realizations for profinite groups which are infinite wreath powers …≀H≀H for some 2-generated finite perfect groups H. This determines the topological rank and improves the estimation for the automaton rank of these wreath powers. We show that we may take H as alternating groups and projective special linear groups." @default.
- W151915566 created "2016-06-24" @default.
- W151915566 creator A5048986684 @default.
- W151915566 date "2012-01-01" @default.
- W151915566 modified "2023-09-25" @default.
- W151915566 title "Automaton Ranks of Some Self-similar Groups" @default.
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- W151915566 doi "https://doi.org/10.1007/978-3-642-28332-1_44" @default.
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