کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587517 1334147 2008 52 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Probabilistic generation of finite simple groups, II
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Probabilistic generation of finite simple groups, II
چکیده انگلیسی

In earlier work it was shown that each nonabelian finite simple group G has a conjugacy class C such that, whenever 1≠x∈G, the probability is greater than 1/10 that G=〈x,y〉 for a random y∈C. Much stronger asymptotic results were also proved. Here we show that, allowing equality, the bound 1/10 can be replaced by 13/42; and, excluding an explicitly listed set of simple groups, the bound 2/3 holds.We use these results to show that any nonabelian finite simple group G has a conjugacy class C such that, if x1, x2 are nontrivial elements of G, then there exists y∈C such that G=〈x1,y〉=〈x2,y〉. Similarly, aside from one infinite family and a small, explicit finite set of simple groups, G has a conjugacy class C such that, if x1, x2, x3 are nontrivial elements of G, then there exists y∈C such that G=〈x1,y〉=〈x2,y〉=〈x3,y〉.We also prove analogous but weaker results for almost simple groups.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 320, Issue 2, 15 July 2008, Pages 443-494