The functor K_2 for multiquadratic number fields
Abstract
Let F and OF be a number field and its ring of integers respectively. Let K2 denote Milnor K-functor. In the paper we describe the structure of the group K2OF/𝕽2F, where 𝕽2F is the Hilbert kernel and F is multiquadratic extension of the rational number field. Moreover, we give some characterization of fields with trivial group K2OF/𝕽2F. At the end we make some remarks on p-rank of K2OF and divisibility of the ideal class group by 2.
References
2. S. Chaładus, Functor K_2 dla wybranych pierścieni, Praca doktorska, Instytut Matematyki Uniwersytetu Warszawskiego (1979).
3. J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Studies 72, (1971).
4. D. Quillen, Higher K-theory for categories with exact sequences, Proc. of the Symp. New developments in topology, Oxford (1972), 95-103.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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