Geodesic
Defining relations of the special unitary group over a quadratic extension of an ordered Euclidean field
Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 415-419 
Zh. S. Satarov. Defining relations of the special unitary group over a quadratic extension of an ordered Euclidean field. Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 415-419. http://geodesic.mathdoc.fr/item/SM_1986_54_2_a7/
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     title = {Defining relations of the special unitary group over a~quadratic extension of an ordered {Euclidean} field},
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     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_2_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $k$ be an ordered Euclidean field (i.e., an ordered field in which the group of nonzero squares coincides with the group of positive elements) and $K$ its quadratic extension. Further, let $\overline\xi$ denote the image of the element $\xi$ under the nontrivial automorphism of the extension $K/k$. We consider the special unitary group $SU(n, K)$ of degree $n\geqslant2$ over the field $K$, i.e., the subgroup of matrices $a$ of the general linear group $GL(n, K)$ for which $aa^*=e$ and $\det a=1$, where $^*$ denotes taking conjugate-transpose, i.e., $(a^*)_{ij}=\overline a_{ji}$. Defining relations in a certain natural system of generators are found for the group $SU(n,\, K)$, $n\geqslant2$. Bibliography: 8 titles.

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[3] Noskov G. A., “Porozhdayuschie elementy i opredelyayuschie sootnosheniya simplekticheskikh grupp nad nekotorymi koltsami”, Matem. zametki, 16:2 (1974), 237–246 | MR | Zbl

[4] Romanovskii N. S., “Obrazuyuschie i opredelyayuschie sootnosheniya polnoi lineinoi gruppy nad lokalnym koltsom”, Sib. matem. zhurn., 13:4 (1971), 922–925 | MR

[5] Satarov Zh. S., “Opredelyayuschie sootnosheniya v unitarnoi gruppe”, Strukturnye svoistva algebraicheskikh sistem, Nalchik, 1981, 97–108

[6] Satarov Zh. S., “Opredelyayuschie sootnosheniya unitarnoi gruppy nad konechnym polem”, Strukturnye svoistva grupp, izd-vo Severo-Osetinsk. un-ta, Ordzhonikidze, 1982, 47–60

[7] Yan Shi-tszyan, “Opredelyayuschie sootnosheniya $n$-mernoi modulyarnoi gruppy”, Beitszin shifan dasaeyu kesyue lunven syuantszi, 1959, 48–70

[8] Green S. M., “Generators and relations for the special linear group over division ring”, Proc. Amer. Math. Soc., 62:2 (1977), 229–232 | DOI | MR | Zbl