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Using fixed-point-free group actions, we set up a scheme to define nestedclasses of groups indexed over ordinals. Restricting to cellular actions onCW-complexes, we find new classes as well as new characterizations for somewell-known classes, such as virtually polycyclic groups. We generalizeproperties of the virtual cohomological dimension of a group to groups withjump (co)homology and prove that a core subclass of a new class of groups hasjump (co)homology.

New Action-Induced Nested Classes of Groups and Jump (Co)homology