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Goldschmidt’s 2-signalizer functor theorem

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Abstract

A solvableA-signalizer functorϑ assigns to any non-identity elementx of the abelian 2-subgroupA of the finite groupG anA-invariant solvable 2′-subgroupθ(C G(x)) ofC G(x) such thatθ(C G(x)) ∩C G(y) ⊆ϑ(C G(y)) for allx, y ∈ A #.θ is called complete ifG has a solvableA-invariant 2′-subgroupK=θ(G) such thatC k(x)=θ(C G(x)) for everyx ∈ A#.

This note contains an alternate proof of the completeness theorem below.

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Authors and Affiliations

  1. Mathematisches Seminar der Universität, 23 Kiel, Federal Republic of Germany

    Helmut Bender

Authors
  1. Helmut Bender
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Additional information

This research originated in September 1973 while the author was visiting the University of Tel Aviv on a grant from the Deutsche Forschungsgemeinschaft.

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Bender, H. Goldschmidt’s 2-signalizer functor theorem. Israel J. Math. 22, 208–213 (1975). https://doi.org/10.1007/BF02761590

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  • DOI: https://doi.org/10.1007/BF02761590

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