On the Image of a Word Map with Constants of a Simple Algebraic Group. II

The paper continues the study of images of word maps with constants ${\tilde{w}}_{\Sigma}:{G}^n\to G$ of a simple algebraic group G, started by F. Gnutov and N. Gordeev (2019). It is proved that for adjoint simple algebraic groups of type B_l, C_l, F₄, G₂ over a field of characteristic ≠ 2, 3, the map $\pi \circ \tilde{w},$ where ${\tilde{w}}_{\Sigma}$ is word map without small constants and π : G → T/W is the factorization map, is a constant map if and only if w_Σ = vgv⁻¹, where g ∈ G and v is a word with constants.