Rendiconti del Seminario Matematico della Università di Padova

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Volume 123, 2010, pp. 233–247
DOI: 10.4171/RSMUP/123-12

Published online: 2010-06-30

Cycles and Bipartite Graph on Conjugacy Class of Groups

Bijan Taeri

Let G be a finite non abelian group and B(G) be the bipartite divisor graph of a finite group related to the conjugacy classes of G. We prove that B(G) is a cycle if and only if B(G) is a cycle of length 6 and GA × SL2(q), where A is abelian, and q ∈ {4,8}. We also prove that if G/Z(G) is simple, where Z(G) is the center of G, then B(G) has no cycle of length 4 if and only if GA × SL2(q), where q ∈ {4,8}.

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Taeri Bijan: Cycles and Bipartite Graph on Conjugacy Class of Groups. Rend. Sem. Mat. Univ. Padova 123 (2010), 233-247. doi: 10.4171/RSMUP/123-12