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Overgroups of exterior powers of an elementary group. levels

Overgroups of exterior powers of an elementary group. levels

ABSTRACTWe prove a first part of the standard description of groups H lying between an exterior power of an elementary group mEn⁡(R) and a general linear group GL(nm)⁡(R) for a commutative ring R,2∈R∗ and n⩾3m. The description uses the classical notion of a level: for every group H we find …