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

Masaharu Morimoto

doi:10.2969/jmsj/06220623

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

Masaharu Morimoto

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we construct nontrivial pairs of script G -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. 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 ℘(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.

Original language	English
Pages (from-to)	623-647
Number of pages	25
Journal	Journal of the Mathematical Society of Japan
Volume	62
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/06220623
Publication status	Published - Apr 2010
Externally published	Yes

Keywords

Gap condition
Laitinen's conjecture
Representation
Smith equivalence
Tangent space

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06220623

Cite this

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abstract = "In this paper we construct nontrivial pairs of script G -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. 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 ℘(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.",

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AB - In this paper we construct nontrivial pairs of script G -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. 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 ℘(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.

KW - Gap condition

KW - Laitinen's conjecture

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KW - Tangent space

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

Abstract

Keywords

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