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The Number of Isomorphism Classes of Finite Groups with Given Element Orders |
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| Authors: | H. Deng M. S. Lucido W. Shi |
| Affiliation: | (1) Department of Computer Science, Southwest Normal University, Chongqing, 400715, People's Republic of China;(2) Dipartimento di Matematica e Informatica, Universita di Udine, via delle Scienze 208, I-33100 Udine, Italy;(3) Institute of Mathematics, Southwest Normal University, Chongqing, 400715, People's Republic of China |
| Abstract: | Let G be a finite group and  e(G) the set of element orders of G. Denote by h(e(G)) the number of isomorphism classes of finite groups H satisfying e(H) = e(G). We prove that if G has at least three prime graph components, then h(e(G)) {1,  }. |
| Keywords: | finite group set of element orders of a group prime graph |
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