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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Smith equivalent $ {\pmb{{\rm {Aut}}(A_6)}}$-representations are isomorphic


Author: Masaharu Morimoto
Journal: Proc. Amer. Math. Soc. 136 (2008), 3683-3688
MSC (2000): Primary 57S17, 57S25, 55M35, 20C15
Published electronically: June 3, 2008
MathSciNet review: 2415055
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Abstract: Many authors, e.g. M. Atiyah, R. Bott, J. Milnor, G. Bredon, S. Cappell, J. Shaneson, C. Sanchez, T. Petrie, E. Laitinen, K. Pawałowski, R. Solomon and so on, studied Smith equivalent representations for finite groups. Observing their results, E. Laitinen conjectured that nonisomorphic Smith equivalent real $ G$-modules exist if $ a_G$, the number of real conjugacy classes of elements not of prime power order in $ G$, is greater than or equal to $ 2$. This paper shows that in the case $ G = {\rm {Aut}}(A_6)$, $ a_G = 2$ any two Smith equivalent real $ G$-modules are isomorphic.


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Additional Information

Masaharu Morimoto
Affiliation: Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushimanaka, Okayama, 700-8530 Japan
Email: morimoto@ems.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-08-08891-6
PII: S 0002-9939(08)08891-6
Received by editor(s): January 24, 2006
Received by editor(s) in revised form: July 7, 2006
Published electronically: June 3, 2008
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (Kakenhi) 18540086
Dedicated: Dedicated to Professor Katsuhiro Komiya on his 60th birthday
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.