Local-global invariants of finite and infinite groups: around Burnside from another side. (English) Zbl 1304.20049
Summary: 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.
MSC:
| 20E36 | Automorphisms of infinite groups |
| 20D45 | Automorphisms of abstract finite groups |
| 20E25 | Local properties of groups |
| 20F28 | Automorphism groups of groups |
| 20-02 | Research exposition (monographs, survey articles) pertaining to group theory |
| 20J06 | Cohomology of groups |
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