2011/10/28 by Rieuwert J. Blok, Blok, Rieuwert J., Stephen Gagola III +1
Mathematics · #20F05 #20F55 #20N05 #51E99 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:20F05 #msc:20F55 #msc:20N05 #msc:51E99
paper · pdf · doi:10.48550/arxiv.1110.6390
Keywords: Coxeter groups, amalgams, Moufang loops, generators and relations
arxiv created 2011/10/28 · arxiv updated 2011/10/31
In 1974 Orin Chein discovered a new family of Moufang loops which are now called Chein loops. Such a loop can be created from any group W together with ℤ2 by a variation on a semi-direct product. We study these loops in the case where W is a Coxeter group and show that it has what we call a Chein-Coxeter system, a small set of generators of order 2, together with a set of relations closely related to the Coxeter relations and Chein relations. As a result we are able to give amalgam presentations for Coxeter-Chein loops. This is to our knowledge the first such presentation for a Moufang loop.