Geodesic
2-Primary Exponent Bounds for Lie Groups of Low Rank
Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 119-132

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Exponent information is proven about the Lie groups $SU(3),\,SU(4),\,Sp(2)$ , and ${{G}_{2}}$ by showing some power of the $H$ -space squaring map (on a suitably looped connected-cover) is null homotopic. The upper bounds obtained are $8,\,32,\,64$ , and ${{2}^{8}}$ respectively. This null homotopy is best possible for $SU(3)$ given the number of loops, off by at most one power of 2 for $SU(4)$ and $Sp(2)$ , and off by at most two powers of 2 for ${{G}_{2}}$ .
DOI : 10.4153/CMB-2004-013-x
Mots-clés : 55Q52, Lie group, exponent 
Theriault, Stephen D. 2-Primary Exponent Bounds for Lie Groups of Low Rank. Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 119-132. doi: 10.4153/CMB-2004-013-x
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     year = {2004},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-013-x/}
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