Abstract
The invariant theory of finite groups has enjoyed considerable recent interest, as the appearance of the books by Benson [18] and Smith [225] and of many articles on the subject show. In this chapter we focus on computational aspects. As in Chapter 2, the central goal is the calculation of a finite set of generators for the invariant ring, but we will also address some interesting properties which invariant rings of finite groups may or may not have, and how they can be tackled algorithmically. Almost all algorithms treated in this chapter have implementations in various computer algebra systems. Here is an (almost certainly incomplete) list of computer algebra packages that are devoted to invariant theory mostly of finite groups, ordered chronologically.
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