منابع مشابه
On 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...
متن کاملBurnside Groups in Knot Theory
Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation. In Kirby’s problem list, this question is called The Montesinos-Nakanishi 3-move conjecture. We define the nth Burnside group of a link and use the 3rd Burnside group to answer Nakanishi’s question. One of the oldest elementary formulated problems in classical Knot Theory is the 3move conjecture of Nakanishi. A 3-move...
متن کاملOn the Burnside Problem for Groups of Even Exponent
The Burnside problem about periodic groups asks whether any finitely generated group with the law x ≡ 1 is necessarily finite. This is proven only for n ≤ 4 and n = 6. A negative solution to the Burnside problem for odd n ≫ 1 was given by Novikov and Adian. The article presents a discussion of a recent solution of the Burnside problem for even exponents n ≫ 1 and related results. 1991 Mathemati...
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 کاملThe Burnside Groups and Small Cancellation Theory
In a pair of recent articles, the author develops a general version of small cancellation theory applicable in higher dimensions ([5]), and then applies this theory to the Burnside groups of sufficiently large exponent ([6]). More specifically, these articles prove that the free Burnside groups of exponent n ≥ 1260 are infinite groups which have a decidable word problem. The structure of the fi...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1973
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700043434