Abstract
In this paper we construct nontrivial pairs of -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 -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.
Citation
Masaharu MORIMOTO. "Nontrivial P(G)-matched -related pairs for finite gap Oliver groups." J. Math. Soc. Japan 62 (2) 623 - 647, April, 2010. https://doi.org/10.2969/jmsj/06220623
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