On Samelson products in p-localized unitary groups |
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Authors: | Hiroaki Hamanaka |
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Institution: | Department of Natural Science, Hyogo University of Teacher Education, Kato, Hyogo 673-1494, Japan |
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Abstract: | The unitary group U(n) has elements εi∈π2i+1(U(n)) (0?i?n−1) of its homotopy groups in the stable range. In this paper we show that certain multi Samelson products of type 〈εi,〈εj,εk〉〉 are non-trivial. This leads us to the result that the nilpotency class of the group of the self homotopy set SU(n),SU(n)] is no less than 3, if 4?n. Also by the power of generalized Samelson products, we can see the further result that, for a prime p and an integer n=pk, nilSU(n),SU(n)](p)?3, if (1) p?7 or (2) p=5 and n≡0 or 1mod4. |
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Keywords: | 55Q15 |
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