Abstract
Let G be a finite group and π e(G) the set of element orders of G. Denote by h(π e(G)) the number of isomorphism classes of finite groups H satisfying π e(H) = π e(G). We prove that if G has at least three prime graph components, then h(π e (G))∈{1, ∞}.
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Deng, H., Lucido, M.S. & Shi, W. The Number of Isomorphism Classes of Finite Groups with Given Element Orders. Algebra and Logic 41, 39–46 (2002). https://doi.org/10.1023/A:1014658001689
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DOI: https://doi.org/10.1023/A:1014658001689