2025/10/08 by Bergman, George M.
#03B25 #08A40 (Secondary) #20M05 (Primary) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2510.07617
Let be the free monoid on a generating set X, and suppose one adjoins to universal 2-sided inverses to a finite set S of its elements. We note an elementary algorithm which yields a normal form for elements of the resulting monoid M. We then show that if S is allowed to be infinite, a similar normal form exists, though it cannot necessarily be computed algorithmically. We raise a couple of questions. We note work by others on the related topic of monoids presented by finite families of relations of the form w = 1.