کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658843 | 1344288 | 2013 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On topologizable and non-topologizable groups
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A group G is called hereditarily non-topologizable if, for every H⩽GH⩽G, no quotient of H admits a non-discrete Hausdorff topology. We construct first examples of infinite hereditarily non-topologizable groups. This allows us to prove that c-compactness does not imply compactness for topological groups. We also answer several other open questions about c-compact groups asked by Dikranjan and Uspenskij. On the other hand, we suggest a method of constructing topologizable groups based on generic properties in the space of marked k-generated groups. As an application, we show that there exist non-discrete quasi-cyclic groups of finite exponent; this answers a question of Morris and Obraztsov.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 160, Issue 16, 1 October 2013, Pages 2104–2120
Journal: Topology and its Applications - Volume 160, Issue 16, 1 October 2013, Pages 2104–2120
نویسندگان
Anton A. Klyachko, Alexander Yu. Olshanskii, Denis V. Osin,