In this paper we construct nontrivial pairs of $\mathfrak{S}$ -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 $\mathfrak{S}$ -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.
Publié le : 2010-04-15
Classification:
Smith equivalence,
Laitinen's conjecture,
tangent space,
representation,
gap condition,
57S25,
55M35,
57S17,
20C15
@article{1273236715,
author = {MORIMOTO, Masaharu},
title = {Nontrivial P(G)-matched $\mathfrak{S}$ -related pairs for finite gap Oliver groups},
journal = {J. Math. Soc. Japan},
volume = {62},
number = {1},
year = {2010},
pages = { 623-647},
language = {en},
url = {http://dml.mathdoc.fr/item/1273236715}
}
MORIMOTO, Masaharu. Nontrivial P(G)-matched $\mathfrak{S}$ -related pairs for finite gap Oliver groups. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp. 623-647. http://gdmltest.u-ga.fr/item/1273236715/