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Let X(r) and G(q) be finite groups of Lie type and r and q be coprime. If G(q) is embedded in X(r), then the Landazuri-Seitz-Zalesskii theorem implies that G(q) is small relative to X(r). We formalize this observation and illustrate how it can be used with some applications.

Bounds on the order of cross characteristic subgroups of the finite simple groups of Lie type