Some products in fusion systems and localities

The theory of saturated fusion systems resembles in many parts the finite groups. However, some concepts from group are difficult to translate systems. For example, products normal subsystems with other only defined special cases. In this paper localities is used prove following result: Suppose F \mathcal {F} a system over alttext="p"> p encoding="application/x-tex">p -group alttext="upper S"> S encoding="application/x-tex">S . If E"> mathvariant="script">E {E} subsystem T less-than-or-equal-to T ≤ encoding="application/x-tex">T\leq S , and D"> mathvariant="script">D {D} subnormal N Subscript script F Baseline left-parenthesis right-parenthesis"> N ( stretchy="false">) encoding="application/x-tex">N_\mathcal {F}(T) R R encoding="application/x-tex">R\leq then there E {E}\mathcal R"> encoding="application/x-tex">TR which plays role product It shown along way that closely related naturally arising certain attached