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In this paper we present an algorithm for determining whether a subgroup H ofa non-connected reductive group G is G-completely reducible. The algorithmconsists of a series of reductions; at each step, we perform operationsinvolving connected groups, such as checking whether a certain subgroup of G^0is G^0 -cr. This essentially reduces the problem of determining G-completereducibility to the connected case.

G-complete reducibility in non-connected groups