Submission: 2013, Aug 3
The first section of this paper is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. The appendix contains formulations of some open problems and the relevant comments.
2010 Mathematics Subject Classification: 20E07, 14E07
Keywords and Phrases: Jordan group, Cremona group, automorphism group, birational map
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