Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of Suzuki's simple groups


Author: Wu Jie Shi
Journal: Proc. Amer. Math. Soc. 114 (1992), 589-591
MSC: Primary 20D06
DOI: https://doi.org/10.1090/S0002-9939-1992-1074758-0
MathSciNet review: 1074758
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this short paper we have characterized Suzuki's simple groups $ {S_z}({2^{2m + 1}}),m \geqslant 1$ using only the set $ {\pi _e}(G)$ of orders of elements in the group $ G$. That is, we have

Theorem 2. Let $ G$ be a finite group. Then $ G \simeq {S_z}({2^{2m + 1}}),m \geqslant 1$ if and only if $ {\pi _e}(G) = \{ 2,4,all\;factors\;of\;{\text{(}}{{\text{2}}^{2m + 1}}{\text{ ... ...ext{2}}^{2m + 1}} - {2^{m + 1}} + 1),\;and\;({2^{2m + 1}} + {2^{m + 1}} + 1)\} $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D06

Retrieve articles in all journals with MSC: 20D06


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1074758-0
Article copyright: © Copyright 1992 American Mathematical Society