A characterization of Suzuki’s simple groups

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 ${\pi _e}(G) = \{ 2,4,all\;factors\;of\;{\text {(}}{{\text {2}}^{2m + 1}}{\text { - 1),(}}{{\text {2}}^{2m + 1}} - {2^{m + 1}} + 1),\;and\;({2^{2m + 1}} + {2^{m + 1}} + 1)\}$.