On 3-transposition groups generated by $\sigma$-involutions associated to c=4/5 Virasoro vectors

In this paper, we show that $\sigma$-involutions associated to extendable c=4/5 Virasoro vectors generate a 3-transposition group in the automorphism group of a vertex operator algebra (VOA). Several explicit examples related to lattice VOA are also discussed in details. In particular, we show that the automorphism group of the VOA $V_{K_{12}}^{\widehat{\nu }}$ associated to the Coxeter Todd lattice $K_{12}$ contains a subgroup isomorphic to ${}^{+}{\mathrm{\Omega }}^{-}(8,3)$.