An especially important class of objects in GAP are those whose underlying mathematical abstraction is that of a structured set, for example a group, a conjugacy class, or a vector space. Such objects are called domains. The equality relation between domains is always equality as sets, so that two domains are equal if and only if they contain the same elements.
Domains play a central role in GAP. In a sense, the only reason that GAP supports objects such as integers and permutations is the wish to form domains of them and compute the properties of those domains.
Domains are described in Chapter Domains and their Elements.
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GAP 4 manual