Displaying 361 – 380 of 664

Showing per page

Presentations of finite simple groups: a computational approach

Robert Guralnick, William M. Kantor, Martin Kassabov, Alexander Lubotzky (2011)

Journal of the European Mathematical Society

All finite simple groups of Lie type of rank n over a field of size q , with the possible exception of the Ree groups 2 G 2 ( q ) , have presentations with at most 49 relations and bit-length O ( 𝚕𝚘𝚐 n + 𝚕𝚘𝚐 q ) . Moreover, A n and S n 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 + 𝚕𝚘𝚐 q ) .

Presentations of surface braid groups by graphs

Paolo Bellingeri, Vladimir Vershinin (2005)

Fundamenta Mathematicae

We extend and generalise Sergiescu's results on planar graphs and presentations for the braid group Bₙ to other topological generalisations of Bₙ.

Q-perfect groups and universal Q-central extensions.

Ronald Brown (1990)

Publicacions Matemàtiques

Using results of Ellis-Rodríguez Fernández, an explicit description by generators and relations is given of the mod q Schur multiplier, and this is shown to be the kernel of a universal q-central extension in the case of a q-perfect group, i.e. one which is generated by commutators and q-th powers. These results generalise earlier work [by] K. Dennis and Brown-Loday.

Quasibases of p -groups

Otto Mutzbauer, Elias Toubassi (1999)

Rendiconti del Seminario Matematico della Università di Padova

Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

Victor Gerasimov, Leonid Potyagailo (2013)

Journal of the European Mathematical Society

We describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using the Floyd completion we further prove that the property of relative hyperbolicity is invariant under quasi-isometric maps. If a finitely generated group H admits a quasi-isometric map ϕ into a relatively hyperbolic group G then H is itself relatively hyperbolic with respect to a system of subgroups whose image under ϕ is situated within a uniformly bounded distance...

Random walks on finite rank solvable groups

Ch. Pittet, Laurent Saloff-Coste (2003)

Journal of the European Mathematical Society

We establish the lower bound p 2 t ( e , e ) exp ( t 1 / 3 ) , for the large times asymptotic behaviours of the probabilities p 2 t ( e , e ) of return to the origin at even times 2 t , for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to r .)

Currently displaying 361 – 380 of 664