Finite simple groups as expanders.
نویسندگان
چکیده
We prove that there exist k in and 0 < epsilon in such that every non-abelian finite simple group G, which is not a Suzuki group, has a set of k generators for which the Cayley graph Cay(G; S) is an epsilon-expander.
منابع مشابه
Finite Simple Groups of Lie Type as Expanders
are uniform expanders. Nikolov [N] proved that every classical group is a bounded product of SLn(q)’s (with possible n = 2, but the proof shows that if the Lie rank is sufficiently high, say ≥ 14, one can use SLn(q) with n ≥ 3). Bounded product of expander groups are uniform expanders. Thus together, their results cover all classical groups of high rank. So, our Theorem is new for classical gro...
متن کاملSymmetric Groups and Expanders
We construct an explicit generating sets Fn and F̃n of the alternating and the symmetric groups, which make the Cayley graphs C(Alt(n), Fn) and C(Sym(n), F̃n) a family of bounded degree expanders for all sufficiently large n. These expanders have many applications in the theory of random walks on groups and other areas of mathematics. A finite graph Γ is called an ǫ-expander for some ǫ ∈ (0, 1), ...
متن کاملCayley Graph Expanders and Groups of Finite Width
We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders. Our first family defines a tower of coverings (with covering indices equals 2) and our second family is given as Cayley graphs of finite groups with very short presentations with only 2 generators and 4 relations. Both families are based on particular finite q...
متن کاملExplicit expanders with cutoff phenomena
The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph. The first example of a family of bounded-degree graphs where the random walk exhibits cutoff in total-variation was provided only very recently, when the aut...
متن کاملClassification of finite simple groups whose Sylow 3-subgroups are of order 9
In this paper, without using the classification of finite simple groups, we determine the structure of finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 103 16 شماره
صفحات -
تاریخ انتشار 2006