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Proceedings of the American Mathematical Society
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Smith equivalent $ {\pmb{{\rm {Aut}}(A_6)}}$-representations are isomorphic

Author(s): Masaharu Morimoto
Journal: Proc. Amer. Math. Soc. 136 (2008), 3683-3688.
MSC (2000): Primary 57S17, 57S25, 55M35, 20C15
Posted: June 3, 2008
MathSciNet review: 2415055
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Abstract | References | Similar articles | Additional information

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: 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
Posted: 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
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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