EuDML | Browse

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.

Presentations of the Amalgamated Free Product of two Infinite Cycles.

Donald J. Collins (1978)

Mathematische Annalen

Preservation and Distortion of Area in Finitely Presented Groups.

S.M. Gersten (1996)

Geometric and functional analysis

Primary graded groups with systems of complemented subgroups.

Vedernikov, V.A., Savicheva, G.V. (2008)

Sibirskij Matematicheskij Zhurnal

Primitives in the Free Group on Two Generators.

R.P. Osborne, H. Zieschang (1981)

Inventiones mathematicae

Problèmes d 'associativité des monoïdes et problèmes des mots pour les groupes

Dov Tamari (1962/1963)

Séminaire Dubreil. Algèbre et théorie des nombres

Prodotti di sottogruppi mutuamente permutabili

Enrico Jabara (2003)

Rendiconti del Seminario Matematico della Università di Padova

Productivity of the Zariski topology on groups

Dikran N. Dikranjan, D. Toller (2013)

Commentationes Mathematicae Universitatis Carolinae

This paper investigates the productivity of the Zariski topology $ℨ_{G}$ of a group $G$ . If $𝒢 = {G_{i} ∣ i \in I}$ is a family of groups, and $G = \prod_{i \in I} G_{i}$ is their direct product, we prove that $ℨ_{G} \subseteq \prod_{i \in I} ℨ_{G_{i}}$ . This inclusion can be proper in general, and we describe the doubletons $𝒢 = {G_{1}, G_{2}}$ of abelian groups, for which the converse inclusion holds as well, i.e., $ℨ_{G} = ℨ_{G_{1}} \times ℨ_{G_{2}}$ . If $e_{2} \in G_{2}$ is the identity element of a group $G_{2}$ , we also describe the class $Δ$ of groups $G_{2}$ such that $G_{1} \times {e_{2}}$ is an elementary algebraic subset of $G_{1} \times G_{2}$ for every group $G_{1}$ . We show among others, that $Δ$ is stable...

Currently displaying 1201 – 1220 of 2186

Previous Page 61 Next

Displaying 1201 – 1220 of 2186

Positively finitely generated groups.

Positively ramified extensions of algebraic number fields.

Positiv-zerlegte p-Erweiterungen algebraischer Zahlkörper.

Powers of a product of commutators as products of squares.

Powers of commutators as products of squares.

Prégroupes de mots et problème des mots

Présentation de certains couples fischériens de type classique

Presentations for the punctured mapping class groups in terms of Artin groups.

Presentations of finite simple groups: a computational approach