Burnside groups and 𝑛-moves for links

Abstract

M. K. Da̧bkowski and J. H. Przytycki introduced the n n th Burnside group of a link, which is an invariant preserved by n n -moves. Using this invariant, for an odd prime p p , they proved that there are links which cannot be reduced to trivial links via p p -moves. It is generally difficult to determine if p p th Burnside groups associated to a link and the corresponding trivial link are isomorphic. In this paper, we give a necessary condition for the existence of such an isomorphism. Using this condition we give a simple proof for their results that concern p p -move reducibility of links.