Apr, 2010
Nontrivial P(G)-matched G-related pairs for finite gap Oliver groups
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
- Volume
- 62
- Number
- 2
- First page
- 623
- Last page
- 647
- Language
- English
- Publishing type
- DOI
- 10.2969/jmsj/06220623
- Publisher
- MATH SOC JAPAN
In this paper we construct nontrivial pairs of G-related (i.e. Smith equivalent) real G-modules for the group G = P Sigma L(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 P(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.
- Link information
- ID information
-
- DOI : 10.2969/jmsj/06220623
- ISSN : 0025-5645
- Web of Science ID : WOS:000277423500007