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In this paper we study groups definable in existentially closed partialdifferential fields of characteristic 0 with an automorphism which commuteswith the derivations. In particular, we study Zariski dense definable subgroupsof simple algebraic groups, and show an analogue of Phyllis Cassidy's resultfor partial differential fields. We also show that these groups have a smallestdefinable subgroup of finite index.

Groups definable in partial differential fields with an automorphism