Open Access
April, 2010 Nontrivial P(G)-matched S -related pairs for finite gap Oliver groups
J. Math. Soc. Japan 62(2): 623-647 (April, 2010). DOI: 10.2969/jmsj/06220623


In this paper we construct nontrivial pairs of S -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. Pawałowski-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 P(G)-matched pair consisting of S -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.


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Masaharu MORIMOTO. "Nontrivial P(G)-matched S -related pairs for finite gap Oliver groups." J. Math. Soc. Japan 62 (2) 623 - 647, April, 2010.


Published: April, 2010
First available in Project Euclid: 7 May 2010

zbMATH: 1260.57053
MathSciNet: MR2662855
Digital Object Identifier: 10.2969/jmsj/06220623

Primary: 57S25
Secondary: 20C15 , 55M35 , 57S17

Keywords: gap condition , Laitinen's conjecture , representation , Smith equivalence , tangent space

Rights: Copyright © 2010 Mathematical Society of Japan

Vol.62 • No. 2 • April, 2010
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