The computation of the rank of diagram groups constructed from semigroup presentation
Adel Mohammad Al-Odhari · International Mathematical Forum · 2013
Copyright © 2013 A. M. Al-Odhari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we continue our study on the result of Kilibarda, “the diagram group), ( wSD is isomorphic to the fundamental group)),((1 wSKπ of the)(complex 2 SK − with the basepoint w, where S is a monoid presentation and w is positive word over alphabet of S ” to construct of the first)(complex NK of diagram group from the semigroup presentation of natural numbers with repeating generators. We will show the diagram group with positive word w 2 ≥ is free of rank 1 2)2)1( (), ( +⎥⎦ ⎡ −−⋅ = nmnmn mμ, where n the numbers of generators in