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The (2, 3)-generation of the finite 8-dimensional orthogonal groups

机译:The (2, 3)-generation of the finite 8-dimensional orthogonal groups

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摘要

Abstract We construct (2,3)(2,3) -generators for the finite 8-dimensional orthogonal groups, proving the following results: the groups Ω8+⁢(q)Omega_{8}^{+}(q) and P⁢Ω8+⁢(q)mathrm{P}Omega_{8}^{+}(q) are (2,3)(2,3) -generated if and only if q≥4qgeq 4 ; the groups Ω8-⁢(q)Omega_{8}^{-}(q) and P⁢Ω8-⁢(q)mathrm{P}Omega_{8}^{-}(q) are (2,3)(2,3) -generated for all q≥2qgeq 2 .

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