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Dec 19, 2016 at 14:47 comment added Jim Humphreys @Tobias: Thanks for adding the essential word "connected" here. The standard example is a special linear group, which usually has a nontrivial finite center (not connected) but is considered "simple" as an algebraic group. This is the definition I used in my 1975 book, though such conventions about the term "simple" always need to be stated explicitly.
Dec 19, 2016 at 9:27 comment added Tobias Kildetoft Minor detail: The definition of simple should include "connected" (i.e. no proper normal, closed, connected subgroup).
Dec 15, 2016 at 15:30 vote accept D_S
Dec 14, 2016 at 21:12 history answered Jim Humphreys CC BY-SA 3.0