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A number-theoretic approach to homotopy exponents of SU(n)

Donald M. Davis·Zhi-Wei Sun
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Abstract

We use methods of combinatorial number theory to prove that, for each $n>1$ and any prime $p$, some homotopy group $π_i(SU(n))$ contains an element of order $p^{n-1+ord_p([n/p]!)}$, where $ord_p(m)$ denotes the largest integer $α$ such that $p^α$ divides $m$.

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Donald M. Davis, Zhi-Wei Sun. 2006-11-23. A number-theoretic approach to homotopy exponents of SU(n). https://arxiv.org/abs/math/0508083

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