Virtual braids and permutations

2018/08/30 by Bellingeri, Paolo, Paris, Luis · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1808.10301

Abstract

Let VB_n be the virtual braid group on n strands and let \mathfrakS_n be the symmetric group on n letters. Let n,m ∈ ℕ such that n ≥ 5, m ≥ 2 and n ≥ m. We determine all possible homomorphisms from VB_n to \mathfrakS_m, from \mathfrakS_n to VB_m and from VB_n to VB_m. As corollaries we get that Out(VB_n) is isomorphic to ℤ/2ℤ × ℤ/2ℤ and that VB_n is both Hopfian and co-Hofpian.

Cited by

• Congruence Subgroups of the Virtual Braid Group

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• Algebraic structures among virtual singular braids