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Let M be a compact surface, either orientable or non-orientable. We study the lower central and derived series of the braid and pure braid groups of M in order to determine the values of n for which B_n(M) and P_n(M) are residually nilpotent or residually soluble. First, we solve this problem for the case where M is the 2-torus. We then give a general description of these series for an arbitrary semi-direct product that allows us to calculate explicitly the lower central series of P_2(K), where K is the Klein bottle, and to give an estimate for the derived series of P_n(K). Finally, if M is a non-orientable compact surface without boundary, we determine the values of n for which B_n(M) is residually nilpotent or residually soluble in the cases that were not already known in the literature.
Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n $in$ N for which there exists a surjection between the n-and m-string braid groups of an orientable surface without boundary. This result is ess
We consider exact sequences and lower central series of surface braid groups and we explain how they can prove to be useful for obtaining representations for surface braid groups. In particular, using a completely algebraic framework, we describe the
Let $n, k geq 3$. In this paper, we analyse the quotient group $B_n/Gamma_k(P_n)$ of the Artin braid group $B_n$ by the subgroup $Gamma_k(P_n)$ belonging to the lower central series of the Artin pure braid group $P_n$. We prove that it is an almost-c
We introduce an algorithmic framework to investigate spherical and geodesic growth series of braid groups relatively to the Artins or Birman-Ko-Lees generators. We present our experimentations in the case of three and four strands and conjecture rati
Motivated by the construction of free quandles and Dehn quandles of orientable surfaces, we introduce Dehn quandles of groups with respect to their subsets. As a characterisation, we prove that Dehn quandles are precisely those quandles which embed n