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Parametrized braid groups of Chevalley groups.

Loday, Jean-Louis, Stein, Michael R. (2005)

Documenta Mathematica

Permutability of centre-by-finite groups

Brunetto Piochi (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be a group and $m$ be an integer greater than or equal to $2$ . $G$ is said to be $m$ -permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$ , then $G$ is $(1+[z/2])$ -permutable. More bounds are given on the least $m$ such that $G$ is $m$ -permutable.

P-nilpotent completion is not idempotent.

Geok Choo Tan (1997)

Publicacions Matemàtiques

Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → GP' where GP' = inv lim(G/ΓiG)P. Here Γ2G is the commutator subgroup [G,G] and ΓiG the subgroup [G, Γi−1G] when i > 2. In this paper, we prove that P-nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with ZP coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of...

Poincaré duality groups of dimension two.

Beno Eckmann, Heinz Müller (1980)

Commentarii mathematici Helvetici

Points fixes des automorphismes de groupe hyperbolique

Frédéric Paulin (1989)

Annales de l'institut Fourier

Nous montrons que le sous-groupe des points fixes d’un automorphisme d’un groupe hyperbolique au sens de M. Gromov est de type fini.

Positively finitely generated groups.

Avinoam Mann (1996)

Forum mathematicum

Positiv-zerlegte p-Erweiterungen algebraischer Zahlkörper.

Kay Wingberg (1985)

Journal für die reine und angewandte Mathematik

Powers of a product of commutators as products of squares.

Abdollahi, Alireza (2004)

International Journal of Mathematics and Mathematical Sciences

Powers of commutators as products of squares.

Akhavan-Malayeri, M. (2002)

International Journal of Mathematics and Mathematical Sciences

Présentation de certains couples fischériens de type classique

M.M. Virotte-Ducharme (1993)

Bulletin de la Société Mathématique de France

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.

Currently displaying 1 – 17 of 17