کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665240 1633799 2016 48 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nilprogressions and groups with moderate growth
ترجمه فارسی عنوان
بدون پیشرفت و گروه با رشد متوسط
کلمات کلیدی
رشد چندجمله ای، دوره دو برابر شدن، محدوده قطر، گروه های محدود گروه تقریبی رشد متوسط، زمان مخلوط کردن
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

We show that doubling at some large scale in a Cayley graph implies uniform doubling at all subsequent scales. The proof is based on the structure theorem for approximate subgroups proved by Green, Tao and the first author. We also give a number of applications to the geometry and spectrum of finite Cayley graphs. For example, we show that a finite group has moderate growth in the sense of Diaconis and Saloff-Coste if and only if its diameter is larger than a fixed power of the cardinality of the group. We call such groups almost flat and show that they have a subgroup of bounded index admitting a cyclic quotient of comparable diameter. We also give bounds on the Cheeger constant, first eigenvalue of the Laplacian, and mixing time. This can be seen as a finite-group version of Gromov's theorem on groups with polynomial growth. It also improves on a result of Lackenby regarding property (τ) in towers of coverings. Another consequence is a universal upper bound on the diameter of all finite simple groups, independent of the CFSG.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 289, 5 February 2016, Pages 1008–1055
نویسندگان
, ,