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Let  V  denote a vector space over two-element field  2  with finite positive dimension and endowed with a symplectic form  B . Let SL( V ) denote the special linear group of  V . Let  S  denote a subset of  V . Define Tv( S ) as the subgroup of SL( V ) generated by the transvections with direction α for all α∈ S . Define  G ( S ) as the graph whose vertex set is  S  and where α, β∈ S  are connected whenever  B (α, β)=1. A well-known theorem states that under the assumption that  S  spans  V , the following (i) and (ii) are equivalent:    (i) Tv( S ) is isomorphic to a symmetric group;    (ii)  G ( S ) is a claw-free block graph.    We give an example which shows that this theorem is not true. We also give a modification of this theorem as follows. Assume that  S  is a linearly independent set of  V  and no element of  S  is in the radical of  V . Then (i) and (ii) are equivalent.

CORRECTION OF A THEOREM ON THE SYMMETRIC GROUP GENERATED BY TRANSVECTIONS