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Directed Core graphs and their Up – down Pregroups | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 17, Issue 4, 2006, Pages 68-81 | ||
| Author | ||
| W.S. Jassim | ||
| Abstract | ||
| In this paper we will define the directed core graphs and will give a method to make any core graph a directed core graph (denoted byΓ* (H,T,T*,v*) ). Also we will show that the set of Schreier transversal is the set of all reduced paths in T with labeled y ∈ X ∪ X −1 ei that is in section 2. In section 3 we will show that the elements of the set of generators of the subgroup H of a free group F generated by X = {a,b} are in form of up – down reduced words. In section 4 we will give an example to show the construction of the directed core graph of H. Finally in section 5 we will construct the up – down pregroup of the directed core graphs and then the universal group of the up – down pregroup of the directed core graph is isomorphic to H. | ||
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