Communicated by A. Y. OlshanskiiWe prove that a group with spectrum {1, 2, 3, 4, 5, 8} is locally finite and is isomorphic to M 10 , where M 10 = A 6 · 2 is the 3-transitive Mathieu group of degree 10, i.e. the corresponding maximal subgroup of the sporadic simple group M 11 .
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