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- W2949927077 abstract "This paper contains several results about the structure of the congruence kernel C^(S)(G) of an absolutely almost simple simply connected algebraic group G over a global field K with respect to a set of places S of K. In particular, we show that C^(S)(G) is always trivial if S contains a generalized arithmetic progression. We also give a criterion for the centrality of C^(S)(G) in the general situation in terms of the existence of commuting lifts of the groups G(K_v) for v notin S in the S-arithmetic completion widehat{G}^(S). This result enables one to give simple proofs of the centrality in a number of cases. Finally, we show that if K is a number field and $G$ is K-isotropic then C^(S)(G) as a normal subgroup of widehat{G}^(S) is almost generated by a single element." @default.
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- W2949927077 date "2016-01-01" @default.
- W2949927077 modified "2023-09-24" @default.
- W2949927077 title "On the Congruence Kernel for Simple Algebraic Groups" @default.
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- W2949927077 doi "https://doi.org/10.1134/s0371968516010143" @default.
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