A 2-local characterization of M(22)

Shousaku Abe

doi:10.55937/sut/1252508439

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Home > Journals > SUT J. Math. > Volume 43 > Issue 2 > Article

June 2007 A 2-local characterization of

M(22)

Shousaku Abe

Author Affiliations +

Shousaku Abe¹
¹Department of Mathematical Information Science Tokyo University of Science 1-3 Kagurazaka Shinjuku-ku,Tokyo 162-8601, Japan

SUT J. Math. 43(2): 227-249 (June 2007). DOI: 10.55937/sut/1252508439

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Abstract

Let $G$ be a finite group with $O(G) = 1$ . We show that if $G$ contains a subgroup $A$ isomorphic to ${E_{64}}$ such that ${C_G}(A) = O({N_G}(A)) \times A$ , ${N_G}(A)/{C_G}(A) \cong Sp(6,2)$ , and ${N_G}(A)/O({N_G}(A))$ splits over $(O({N_G}(A))A)/O({N_G}(A))$ , then either $G \cong M(22)$ or $G = {N_G}(A)$ .