Isomorphisms of graph groups
Author: Carl Droms
Journal: Proc. Amer. Math. Soc. 100 (1987), 407-408
MSC: Primary 20F05; Secondary 05C25, 20F12
MathSciNet review: 891135
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Abstract: Given a graph , define the presentation to have generators the vertices of , and a relation for each pair of adjacent vertices. Let be the group with presentation , and given a field , let denote the -algebra with presentation . Given graphs and and a field , it is known that the algebras and are isomorphic if and only if the graphs and are isomorphic. In this paper, we use this fact to prove that if the groups and are isomorphic, then so are the graphs and .