Archiv der Mathematik

, Volume 102, Issue 4, pp 301–312 | Cite as

Finite simple 3′-groups are cyclic or Suzuki groups

  • Imke Toborg
  • Rebecca Waldecker


In this note we prove that all finite simple 3′-groups are cyclic of prime order or Suzuki groups. This is well known in the sense that it is mentioned frequently in the literature, often referring to unpublished work of Thompson. Recently an explicit proof was given by Aschbacher [3], as a corollary of the classification of \({\mathcal{S}_3}\) -free fusion systems. We argue differently, following Glauberman’s comment in the preface to the second printing of his booklet [8]. We use a result by Stellmacher (see [12]), and instead of quoting Goldschmidt’s result in its full strength, we give explicit arguments along his ideas in [10] for our special case of 3′-groups.


Normal Subgroup Maximal Subgroup Prime Order Central Product Characteristic Subgroup 
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© Springer Basel 2014

Authors and Affiliations

  1. 1.Martin-Luther-Universität Halle-Wittenberg Institut für MathematikHalleGermany

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