is there group named Shafarevich-Tate group I,II?why Shafarevich-Tate group III is named?

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The Tate-Shafarevich group is denoted by the cyrillic letter "sha" (like Shafarevich), which looks a bit like III, but it's not a roman numeral three. See Wikipedia.

Side note: this is not at all a Sage question, and you could have found the answer by a simple search on your favourite search engine or on Wikipedia.