Reduced fusion systems over p -groups with abelian subgroup of index p: III

Bob Oliver, Albert Ruiz

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian p-groups with an abelian subgroup of index p. In particular, this gives many new examples illustrating the enormous variety of exotic examples that can arise. In addition, we classify all simple fusion systems over infinite nonabelian discrete p-toral groups with an abelian subgroup of index p. In all of these cases (finite or infinite), we reduce the problem to one of listing all pG-modules (for G finite) satisfying certain conditions: a problem which was solved in the earlier paper [15] using the classification of finite simple groups.
Original languageEnglish
Article number0308210518001075
Pages (from-to)1187-1239
Number of pages53
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume150
Issue number3
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • finite groups
  • finite simple groups
  • fusion
  • modular representations
  • Sylow subgroups
  • COMPACT-GROUPS
  • LIE-GROUPS
  • FINITE-GROUPS
  • CLASSIFICATION
  • HOMOTOPY-THEORY

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