Misc.

Apr, 2010

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

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
  • Masaharu Morimoto

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
DOI
https://doi.org/10.2969/jmsj/06220623
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000277423500007&DestApp=WOS_CPL
ID information
  • DOI : 10.2969/jmsj/06220623
  • ISSN : 0025-5645
  • Web of Science ID : WOS:000277423500007

Export
BibTeX RIS