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The group <math>\pi_p(EU(n))</math> is trivial for all <math>p\ge 1</math>.<br />
'''Proof'''
Let <math>\gamma</math> be a map from the sphere <math>S^p</math> to ''EU(n)''. As <math>S^p</math> is [[compact space|compact]],
there exists <math>k</math> such that <math>\gamma(S^p)</math> is included in <math>F_n(\mathbb{C}^k)</math>. By taking <math>k</math> big enough,
we see that <math>\gamma</math> is homotopic, with respect to the base point, to the constant map.
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