Free Symmetric and Unitary Pairs in Division Rings with Involution
نویسندگان
چکیده
Let D be a division ring with an involution and characteristic different from 2. Then, up to a few exceptions, D contains a free pair of symmetric elements provided that (a) it is finite-dimensional and the center has a finite sufficiently large transcendence degree over the prime field, or (b) the center is uncountable, but not algebraically closed in D. Under conditions (a), if the involution is of the first kind, it is also shown that the unitary subgroup of U(D) contains a free subgroup, with one exception. The methods developed are also used to describe free subgroups in the multiplicative group of a finite-dimensional division ring provided the center has a sufficiently large transcendence degree over its prime field. May, 2002 ICMC-USP
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ورودعنوان ژورنال:
- IJAC
دوره 15 شماره
صفحات -
تاریخ انتشار 2005