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Motivated by the recently introduced concept of a pseudosymmetric braidedmonoidal category, we define the pseudosymmetric group PS_n, as the quotient ofthe braid group B_n by the relations \sigma_i\sigma_{i+1}^{-1}\sigma_i=\sigma_{i+1}\sigma_i^{-1}\sigma_{i+1}, with 1\leq i\leq n-2. It turns out that PS_nis isomorphic to the quotient of B_n by the commutator subgroup [P_n, P_n] ofthe pure braid group P_n (which amounts to saying that [P_n, P_n] coincideswith the normal subgroup of B_n generated by the elements [\sigma_i^2,\sigma_{i+1}^2], with 1\leq i\leq n-2), and that PS_n is a linear group.

A quotient of the braid group related to pseudosymmetric braided categories