کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4658075 1633079 2016 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Topological groups with many small subgroups
ترجمه فارسی عنوان
گروه های توپولوژیک با بسیاری از زیر گروه های کوچک
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
چکیده انگلیسی

We introduce and study a functorial topology on every group G having as a base the family of all subgroups of G. Making use of this topology, we obtain an equivalent description of the small subgroup generating property introduced by Gould [26]; see also Comfort and Gould [6]. This property implies minimal almost periodicity. Answering questions of Comfort and Gould [6], we show that every abelian group of infinite divisible rank admits a group topology having the small subgroup generating property. For unbounded abelian groups of finite divisible rank, we find a new necessary condition for the existence of a group topology having the small subgroup generating property, and we conjecture that this condition is also sufficient.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 200, 1 March 2016, Pages 101–132
نویسندگان
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