@article{b65d6f647dbe47f5a092c8eb43c21a8b,

title = "Burnside groups and n-moves for links",

abstract = "M. K. Dabkowski and J. H. Przytycki introduced the nth Burnside group of a link, which is an invariant preserved by n-moves. Using this invariant, for an odd prime p, they proved that there are links which cannot be reduced to trivial links via p-moves. It is generally difficult to determine if pth 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-move reducibility of links.",

keywords = "Burnside group, Fox coloring, Link, Magnus expansion, Montesinos-Nakanishi 3- move conjecture, Virtual link, Welded link",

author = "Miyazawa, {Haruko A.} and Kodai Wada and Akira Yasuhara",

note = "Funding Information: Received by the editors February 18, 2018, and, in revised form, August 27, 2018, and October 31, 2018. 2010 Mathematics Subject Classification. Primary 57M25, 57M27; Secondary 20F50. Key words and phrases. Link, Burnside group, Magnus expansion, Montesinos–Nakanishi 3-move conjecture, Fox coloring, virtual link, welded link. The second author was supported by a Grant-in-Aid for JSPS Research Fellow (#17J08186) of the Japan Society for the Promotion of Science. The third author was partially supported by a Grant-in-Aid for Scientific Research (C) (#17K05264) of the Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

doi = "10.1090/proc/14470",

language = "English",

volume = "147",

pages = "3595--3602",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "8",

}