Presentations of finite simple groups: A quantitative approach

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Presentations of Finite Simple Groups: a Quantitative Approach

There is a constant C0 such that all nonabelian finite simple groups of rank n over Fq , with the possible exception of the Ree groups G2(3), have presentations with at most C0 generators and relations and total length at most C0(logn + log q). As a corollary, we deduce a conjecture of Holt: there is a constant C such that dimH2(G, M) ≤ C dimM for every finite simple group G, every prime p and ...

متن کامل

Presentations of Finite Simple Groups: a Computational Approach

All nonabelian finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups G2(q), have presentations with at most 49 relations and bit-length O(log n+log q). Moreover, An and Sn have presentations with 3 generators, 7 relations and bit-length O(log n), while SL(n, q) has a presentation with 6 generators, 25 relations and bit-length O(log n + ...

متن کامل

A Simple Classification of Finite Groups of Order p2q2

‎Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p^2q^2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p^2+3p/2+7 groups when Q is an elementary ablian group an...

متن کامل

Presentations of finite simple groups: profinite and cohomological approaches

We prove the following three closely related results: (1) Every finite simple group G has a profinite presentation with 2 generators and at most 18 relations. (2) If G is a finite simple group, F a field and M is an FG-module, then dim H.G;M/ .17:5/ dim M . (3) If G is a finite group, F a field and M is an irreducible faithful FG-module, then dim H.G;M/ .18:5/ dim M . Mathematics Subject Classi...

متن کامل

Finite Presentations of Hyperbolic Groups

Although (G, dS) is not a geodesic metric space, its Cayley graph ΓS(G) is, and it is the geodesics that provide the natural relationship between dS and the Cayley graph. Let G be the vertex set on the Cayley graph. Two vertices g and h are adjacent in ΓS(G) precisely when g −1h ∈ S or h−1g ∈ S, in which case dS(g, h) = 1. Inductively, it follows that dS(g, h) = n precisely when the shortest pa...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of the American Mathematical Society

سال: 2008

ISSN: 0894-0347,1088-6834

DOI: 10.1090/s0894-0347-08-00590-0