Nontrivial ℘(G)-matched script G-related pairs for finite gap Oliver groups

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Abstract

In this paper we construct nontrivial pairs of script G -related (i.e. Smith equivalent) real (G-modules for the group G = PΣL(2,27) and the small groups of order 864 and types 2666, 4666. This and a theorem of K. Pawalowski-R. Solomon together show that Laitinen's conjecture is affirmative for any finite nonsolvable gap group. That is, for a finite nonsolvable gap group G, there exists a nontrivial ℘(G)-matched pair consisting of G-related real G-modules if and only if the number of all real conjugacy classes of elements in G not of prime power order is greater than or equal to 2.

Original languageEnglish
Pages (from-to)623-647
Number of pages25
JournalJournal of the Mathematical Society of Japan
Volume62
Issue number2
DOIs
Publication statusPublished - Apr 1 2010

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Keywords

  • Gap condition
  • Laitinen's conjecture
  • Representation
  • Smith equivalence
  • Tangent space

ASJC Scopus subject areas

  • Mathematics(all)

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