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
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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
Journal: Topology and its Applications - Volume 200, 1 March 2016, Pages 101–132
نویسندگان
Dikran Dikranjan, Dmitri Shakhmatov,