The Extension of Diagram Group over Semigroup Presentation
Kalthom Mahmood Almabrok *
Mathematics Department, Gharyan University, Libya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we will discuss the diagram groups from union of two semigroup presentations namely 2S , =< X,Y : X = Y >, 3S = < a,b,c : a = b, b = c,c = a, > and their two complex graphs will be presented. The covering space will be determined by selecting normal subgroup from diagram group that previously obtained from 2S U3S . Finally, the number of generator and relations of the diagram group can be computed.
Keywords: Generators, relations, diagram groups, semigroup presentation