Rational languages and the Burnside problem
نویسندگان
چکیده
منابع مشابه
Rational Languages and the Burnside Problem
The problem of finding regularity conditions for languages is, via the syntactic monoid, closely related to the classical Burnside problem. This survey paper presents several results and conjectures in this direction as well as on related subjects, including bounded languages, pumping, square-free words, commutativity, and rational power series.
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After many unsuccessful attempts to obtain a proof in the late 30s-early 40s the following weaker version of The Burnside Problem was studied: Is it true that there are only finitely many 7??-generated finite groups of exponent nl In other words the question is whether there exists a universal finite m-generated group of exponent n having all other finite m-generated groups of exponent n as hom...
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J. Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Furthermore, we deduce that certain Burnside groups are non-unitarisable, answering a question raised by G. Pisier.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1985
ISSN: 0304-3975
DOI: 10.1016/0304-3975(85)90156-2