The congruence structure of racks
作者:
Hayley Ryder,
期刊:
Communications in Algebra
(Taylor Available online 1995)
卷期:
Volume 23,
issue 13
页码: 4971-4989
ISSN:0092-7872
年代: 1995
DOI:10.1080/00927879508825511
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
We examine racks from an algebraic viewpoint, concentrating on conned;ions between racks and other, more throughly understood structures such as groups. The fundamental rack is a necessarily complicated object which does not lend itself to detailed study. We therefore focus our attention on congruences on racks which enable us to simplify their structure and study their representation. It is likely that new, easily calculable invariants of links may be derived in this way. (For example, a link in S3 is n-colourable if and only if the fundamental rack is congruent to the dihedral rack of order n [F-R].) The main result states that the congruence structure on any rack may be described by considering certain subgroups of either of two groups naturally associated to the rack.
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