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This article is cited in 5 scientific papers (total in 5 papers)
The Number of Isomorphism Classes of Finite Groups with Given Element Orders
H. Denga, M. S. Lucido, W. Shi a Southwest China Normal University
Abstract:
Let $G$ be a finite group and $\pi_e(G)$ the set of element orders of $G$. Denote by $h(\pi_e(G))$ the number of isomorphism classes of finite groups $H$ satisfying $\pi_e(H)=\pi_e(G)$. We prove that if $G$ has at least three prime graph components, then $h(\pi_e(G))\in\{1, \infty\}$.
Keywords:
finite group, set of element orders of a group, prime graph.
Received: 08.08.2000 Revised: 26.04.2000
Citation:
H. Deng, M. S. Lucido, W. Shi, “The Number of Isomorphism Classes of Finite Groups with Given Element Orders”, Algebra Logika, 41:1 (2002), 70–82; Algebra and Logic, 41:1 (2002), 39–46
Linking options:
https://www.mathnet.ru/eng/al172 https://www.mathnet.ru/eng/al/v41/i1/p70
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Abstract page: | 500 | Full-text PDF : | 140 | References: | 71 | First page: | 1 |
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