The isomorphism between two fundamental groups by Cayley graphs
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LetG1 and G2 be two nite groups and letCay(G1,S1) and Cay(G2,S2) be the corresponding Cayley graphs of these groups, respectively. By [2] and [8], one can dene the fundamental groupπ1(Γ,v) by using any connected graph Γ with a fixed vertex v. In this paper we give sufficient conditions for any two fundamental groups which are obtained by Cayley graphs Cay(G1,S1) and Cay(G2,S2) to be isomorphic. At the final part of the paper, we present some examples of this result.
Abstract
LetG1 and G2 be two nite groups and letCay(G1,S1) and Cay(G2,S2) be the corresponding Cayley graphs of these groups, respectively. By [2] and [8], one can dene the fundamental groupπ1(Γ,v) by using any connected graph Γ with a fixed vertex v. In this paper we give sufficient conditions for any two fundamental groups which are obtained by Cayley graphs Cay(G1,S1) and Cay(G2,S2) to be isomorphic. At the final part of the paper, we present some examples of this result.
참고문헌 (11)
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