Geodesic
Class numbers and groups of algebraic groups. II
Izvestiya. Mathematics, Tome 16 (1981) no. 2, pp. 357-372 Cet article a éte moissonné depuis la source Math-Net.Ru

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The central result of this article is a realization theorem, according to which, for a semisimple indefinite algebraic $K$-group $G$ ($K$ is an algebraic number field) an arbitrary finite abelian group of exponent $f$, where $f$ is the index of the kernel $F$ of the universal covering $\widetilde G\to G$, can be realized as a class group $\mathscr G\operatorname{cl}(\varphi(G))$. In the second part of the article the class number of semisimple groups that are not indefinite (groups of compact type) is investigated. The following general theorem is proved: if $G$ is a semisimple group of compact type of degree $n$, then for any natural number $r$ there exists a lattice $M(r)\subset K^{2n}$ such that $\operatorname{cl}(G^{M(r)})$ is divisible by $r$. Bibliography: 12 titles. 
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V. P. Platonov; A. A. Bondarenko; A. S. Rapinchuk. Class numbers and groups of algebraic groups. II. Izvestiya. Mathematics, Tome 16 (1981) no. 2, pp. 357-372. http://geodesic.mathdoc.fr/item/IM2_1981_16_2_a5/

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