ZJ-theorems for fusion systems

Radha Kessar, Markus Linckelmann

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

For p an odd prime, we generalise the Glauberman-Thompson pnilpotency theorem (Gorenstein, 1980) to arbitrary fusion systems. We de. ne a notion of Qd(p)-free fusion systems and show that if F is a Qd(p)-free fusion system on some finite p-group P, then F is controlled by W( P) for any Glauberman functor W, generalising Glauberman's ZJ-theorem (Glauberman, 1968) to arbitrary fusion systems.
Original languageEnglish
Pages (from-to)3093-3106
Number of pages14
JournalTransactions of the American Mathematical Society
Volume360
Issue number6
DOIs
Publication statusPublished - 25 Jan 2008

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Keywords

  • FINITE-GROUPS
  • SUBGROUP
  • BLOCKS

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