Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.
For a commutative ring with identity, we obtain a complete description of all overgroups of unitary groups U2nR (n ≥ 5), which include symplectic, ordinary orthogonal and standard unitary groups, in linear group GL2nR.
