کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771980 | 1630434 | 2017 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Quantifying residual finiteness of linear groups
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Quantifying residual finiteness of linear groups Quantifying residual finiteness of linear groups](/preview/png/5771980.png)
چکیده انگلیسی
Normal residual finiteness growth measures how well a finitely generated residually finite group is approximated by its finite quotients. We show that any finitely generated linear group Îâ¤GLd(K) has normal residual finiteness growth asymptotically bounded above by (nlogâ¡n)d2â1; notably this bound depends only on the degree of linearity of Î. If char K=0 or K is a purely transcendental extension of a finite field, then this bound can be improved to nd2â1. We also give lower bounds on the normal residual finiteness growth of Î in the case that Î is a finite index subgroup of G(Z) or G(Fp[t]), where G is Chevalley group of rank at least 2. These lower bounds agree with the computed upper bounds, providing exact asymptotics on the normal residual finiteness growth. In particular, finite index subgroups of G(Z) and G(Fp[t]) have normal residual finiteness growth ndimâ¡(G). We also compute the non-normal residual finiteness growth in the above cases; for the lower bounds the exponent dimâ¡(G) is replaced by the minimal codimension of a maximal parabolic subgroup of G.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 480, 15 June 2017, Pages 22-58
Journal: Journal of Algebra - Volume 480, 15 June 2017, Pages 22-58
نویسندگان
Daniel Franz,