Goldschmidt’s 2-signalizer functor theorem
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- Bender, H. Israel J. Math. (1975) 22: 208. doi:10.1007/BF02761590
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A solvableA-signalizer functorϑ assigns to any non-identity elementx of the abelian 2-subgroupA of the finite groupG anA-invariant solvable 2′-subgroupθ(CG(x)) ofCG(x) such thatθ(CG(x)) ∩CG(y) ⊆ϑ(CG(y)) for allx, y ∈ A#.θ is called complete ifG has a solvableA-invariant 2′-subgroupK=θ(G) such thatCk(x)=θ(CG(x)) for everyx ∈ A#.
This note contains an alternate proof of the completeness theorem below.