This expository essay is focused on the Shafarevich-Tate set of a group G. Since its introduction for a finite group by Burnside, it has been rediscovered and redefined more than once. We discuss its various incarnations and properties as well as relationships (some of them conjectural) with other local-global invariants of groups.
Bibliographical noteFunding Information:
This research was supported by the Israel Science Foundation , grant 1207/12 . The author was supported in part by the Minerva Foundation through the Emmy Noether Research Institute of Mathematics . This paper was mainly written during several visits to the MPIM (Bonn) and NCTS (Taipei) in 2008–2012. Support of these institutions is gratefully acknowledged.
- Outer automorphisms of a group
- Shafarevich-Tate set