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On Localized Unstable K1-groups andApplications to Self-homotopy Groups

Published online by Cambridge University Press:  20 November 2018

Daisuke Kishimoto ,
Akira Kono  and
Mitsunobu Tsutaya
Daisuke Kishimoto
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan e-mail: kishi@math.kyoto-u.ac.jp
Akira Kono
Affiliation:
Faculty of Science and Engineering, Doshisha University, Kyoto 610-0321, Japan e-mail: akono@mail.doshisha.ac.jptsutaya@math.kyoto-u.ac.jp
Mitsunobu Tsutaya
Affiliation:
Faculty of Science and Engineering, Doshisha University, Kyoto 610-0321, Japan e-mail: akono@mail.doshisha.ac.jptsutaya@math.kyoto-u.ac.jp
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Abstract

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The method for computing the $p$-localization of the group $\left[ X,\,\text{U}\left( n \right) \right]$, by Hamanaka in 2004, is revised. As an application, an explicit description of the self-homotopy group of $\text{Sp}\left( 3 \right)$ localized at $p\,\ge \,5$ is given and the homotopy nilpotency of $\text{Sp}\left( 3 \right)$ localized at $p\,\ge \,5$ is determined.

Keywords

55P4555P6055Q05Lie groupself-homotopy grouplocalization
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 344 - 356
Copyright
Copyright © Canadian Mathematical Society 2014

References

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