کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587537 1334147 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Connectivity of the Product Replacement Graph of simple groups of bounded Lie rank
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Connectivity of the Product Replacement Graph of simple groups of bounded Lie rank
چکیده انگلیسی

The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertices are the generating k-tuples of the group (for a fixed k).We show that there is a function c(r) such that for any finite simple group of Lie type, with Lie rank r, the Product Replacement Graph of the generating k-tuples is connected for any k⩾c(r).The proof uses results of Larsen and Pink [M.J. Larsen, R. Pink, Finite subgroups of algebraic groups, preprint, 1998] and does not rely on the classification of finite simple groups.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 320, Issue 2, 15 July 2008, Pages 945-960