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Forbidden relations in universal virtual braid groups
Oscar Ocampo, Charalampos Stylianakis
We study natural automorphisms of the universal virtual braid group . These automorphisms induce commuting involutions in the outer automorphism group and generate a subgr…
Universal virtual braid groups
Oscar Ocampo
We introduce the universal virtual braid group , which provides a unified algebraic framework for virtual braid--type structures with types of crossings and admits nat…
Permutational wreath pullbacks and framed braid-type groups
Ênio Leite, Oscar Ocampo
Let be a surjective homomorphism and let be a group. We introduce the \emph{permutational wreath pullback} \[ H \wr_σG = H^n \rtimes_σG, \] where the action…
Powers of half-twists and congruence subgroups of braid groups
Paolo Bellingeri, Celeste Damiani, Oscar Ocampo +1
In this work, we study the relationship between congruence subgroups and the normal closure of , where is the classical generator of $B…
Congruence subgroups of braid groups and crystallographic quotients. Part II
Paolo Bellingeri, Celeste Damiani, Oscar Ocampo +1
Following previous work on congruence subgroups and crystallographic braid groups, we study the lower central series of congruence braid groups related to the braid group , sh…
Congruence subgroups of braid groups and crystallographic quotients. Part I
Paolo Bellingeri, Celeste Damiani, Oscar Ocampo +1
This paper is the first of a two part series devoted to describing relations between congruence and crystallographic braid groups. We recall and introduce some elements belonging t…
Subgroup separability of surface braid groups and virtual braid groups
Kisnney Almeida, Igor Lima, Oscar Ocampo
In this paper, we study subgroup separability (also known as LERF) and related properties for surface braid groups and virtual (singular) braid groups.