منابع مشابه
The Restricted Burnside Problem
In 1902 William Burnside [5] wrote 'A still undecided point in the theory of discontinuous groups is whether the order of a group may be not finite, while the order of every operation it contains is finite'. In modern terminology the most general form of the problem is 'can a finitely generated group be infinite while every element in the group has finite order?'. This question was answered in ...
متن کاملOn the Restricted Burnside Problem
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...
متن کاملRational 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.
متن کاملThe Dixmier Problem, Lamplighters and Burnside Groups
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.
متن کاملOn the Burnside Problem on Periodic Groups
It is proved that the free m-generated Burnside groups B(m, n) of exponent n are infinite provided that m > 1 , n > 248 . In 1902 William Burnside posed the following problem [2]. Does a group G have to be finite provided that G has a finite set of generators and its elements satisfy the identity x" — 1 ? In other words, must a finitely generated group G of exponent n be finite? In the same pap...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1966
ISSN: 0021-8693
DOI: 10.1016/0021-8693(66)90031-7