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Thompson uniqueness theorem

From Wikipedia, the free encyclopedia

In mathematical finite group theory, Thompson's original uniqueness theorem (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementary abelian subgroup of rank 3. Bender (1970) gave a shorter proof of the uniqueness theorem.

References[edit]

  • Bender, Helmut (1970), "On the uniqueness theorem", Illinois Journal of Mathematics, 14 (3): 376–384, doi:10.1215/ijm/1256053074, ISSN 0019-2082, MR 0262351
  • Bender, Helmut; Glauberman, George (1994), Local analysis for the odd order theorem, London Mathematical Society Lecture Note Series, vol. 188, Cambridge University Press, ISBN 978-0-521-45716-3, MR 1311244
  • Feit, Walter; Thompson, John G. (1963), "Solvability of groups of odd order", Pacific Journal of Mathematics, 13: 775–1029, doi:10.2140/pjm.1963.13.775, ISSN 0030-8730, MR 0166261