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Polynomial invariants of 2-component links.

Kunio Murasugi (1985)

Revista Matemática Iberoamericana

Let L = X U Y be an oriented 2-component link in S3. In this paper we will define two different types of polynomials which are ambient isotopic invariants of L. One is associated with a cyclic cover branched along one of their components, an the other is associated with a metabelian cover of L. This invariants are defined for any link unless the linking number lk(X,Y), is ±1.

Polynomials over Q solving an embedding problem

Nuria Vila (1985)

Annales de l'institut Fourier

The fields defined by the polynomials constructed in E. Nart and the author in J. Number Theory 16, (1983), 6–13, Th. 2.1, with absolute Galois group the alternating group A n , can be embedded in any central extension of A n if and only if n ≡ 0 ( m o d 8 ) , or n ≡ 2 ( m o d 8 ) and n is a sum of two squares. Consequently, for theses values of n , every central extension of A n occurs as a Galois group over Q .

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 21 – 40 of 57