  A study of the effective tbW vertex is done in the littlest Higgs model with
T parity that includes the one loop induced weak dipole coefficient f_{2R}. The
top's width, the W-boson helicity in the t-> bW^+ decay as well as the
t-channel and the s-channel modes of single top quark production at the LHC are
then obtained for the tbW coupling. Our calculation is done in the Feynman-'t
Hooft gauge, and we provide details of the analysis, like exact formulas (to
all orders of the expansion variable v/f) of masses and mixing angles of all
the particles involved. Also, a complete and exact diagonalization (and
normalization) of the scalar sector of the model is made.
