#### Volume 6, issue 1 (2002)

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Burnside obstructions to the Montesinos–Nakanishi $3$–move conjecture

### Mieczysław K Dabkowski and Józef H Przytycki

Geometry & Topology 6 (2002) 355–360
 arXiv: math.GT/0205040
##### Abstract

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 $n$th Burnside group of a link and use the 3rd Burnside group to answer Nakanishi’s question; ie, we show that some links cannot be reduced to trivial links by 3–moves.

##### Keywords
knot, link, tangle, 3–move, rational move, braid, Fox coloring, Burnside group, Borromean rings, Montesinos–Nakanishi conjecture, branched cover, core group, lower central series, associated graded Lie ring, skein module
Primary: 57M27
Secondary: 20D99