This article is cited in 2 papers

The Mathieu group $M_{12}$

V. M. Sitnikov

Institute of Mathematics and Mechanics, Academy of Sciences of the USSR

Abstract: Let $G$ be a finite simple non-Abelian group. $t$ is an involution of $G$, and $L=O^2(C_G(t)/O(C_G(t)))$. If the center $Z(L)$ is cyclic and $L/Z(L)\simeq PGL(2,q)$, $q$ odd, then either a Sylow 2-subgroup of $G$ is semidihedral or $C_G(t)\simeq Z_2\times PGL(2,5)$ and $G$ is isomorphic to the Mathieu group $M_{12}$ of degree 12.

Received: 28.05.1973

 English version: Mathematical Notes, 1974, 15:4, 386–390

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