Geodesic
Elementary equivalence of unitary linear groups over fields
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1265-1278.

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In this article it is proved that two unitary linear groups over fields with involutions with skew-symmetric forms of maximal rank are elementary equivalent if and only if they have the same dimension and the fields are elementary equivalent as the fields with involutions. 
@article{FPM_1998_4_4_a7,
     author = {E. I. Bunina},
     title = {Elementary equivalence of unitary linear groups over fields},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1265--1278},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a7/}
}
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E. I. Bunina. Elementary equivalence of unitary linear groups over fields. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1265-1278. http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a7/