A note on groups generated by involutions and sharply 2-transitive groups

George Glauberman, Avinoam Mann, Yoav Segev

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Let G be a group generated by a set C of involutions which is closed under conjugation. Let π be a set of odd primes. Assume that either (1) G is solvable, or (2) G is a linear group. We show that if the product of any two involutions in C is a π-element, then G is solvable in both cases and G = Oπ(G)〈t〉, where t ∈ C. If (2) holds and the product of any two involutions in C is a unipotent element, then G is solvable. Finally we deduce that if G is a sharply 2-transitive (infinite) group of odd (permutational) characteristic, such that every 3 involutions in G generate a solvable or a linear group; or if G is linear of (permutational) characteristic 0, then G contains a regular normal abelian subgroup.

Original languageEnglish
Pages (from-to)1925-1932
Number of pages8
JournalProceedings of the American Mathematical Society
Volume143
Issue number5
DOIs
StatePublished - 1 Jan 2015

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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