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10 papers · 1 filter
Markov and Artin normal form theorem for braid groups
L. A. Bokut, V. V. Chaynikov, K. P. Shum
In this paper we will present the results of Artin--Markov on braid groups by using the Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov-…
Properties of element orders in covers for L(n,q) and U(n,q)
Andrei V. Zavarnitsine
We show that if a finite simple group G isomorphic to PSL(n,q) or PSU(n,q), where either , or q is prime or even, acts on a vector space over a field of the defining charac…
Sylow's theorem for Moufang loops
Alexander N. Grishkov, Andrei V. Zavarnitsine
For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion of the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in th…
Representations of Braid Groups and Generalisations
Valerij G. Bardakov, Paolo Bellingeri
We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particula…
On certain questions of the free group automorphisms theory
Valeriy G. Bardakov, Roman Mikhailov
Certain subgroups of the groups of automorphisms of a free group are considered. Comparing Alexander polynomials of two poly-free groups and we prov…
Extending representations of braid groups to the automorphism groups of free groups
Valerij G. Bardakov
We construct a linear representation of the group IA(F_n) of IA-automorphisms of a free group F_n, an extension of the Gassner representation of the pure braid group P_n. Although…