Finite simple groups with Hall $\{2, r\}$-subgroups, $r \in π(G) \backslash \{2, t\}$, $t \in π(G) $

Abstract

UDC 512.542
We describe finite simple groups with Hall biprimary subgroups of even order that contain Sylow subgroups of odd order of the $G$-group, except one of Sylow's subgroups of odd order.