36.4 Closures of (Sub)groups

creates the group generated by the elements of G and obj. obj can be either an element or a collection of elements, in particular another group.

gap> g:=SmallGroup(24,12);;u:=Subgroup(g,[g.3,g.4]);
Group([ f3, f4 ])
gap> ClosureGroup(u,g.2);
Group([ f2, f3, f4 ])
gap> ClosureGroup(u,[g.1,g.2]);
Group([ f1, f2, f3, f4 ])
gap> ClosureGroup(u,Group(g.2*g.1));
Group([ f1*f2^2, f3, f4 ])

These three functions together with ClosureGroupDefault implement the main methods for ClosureGroup (see ClosureGroup). In the ordering given, they just add elm to the generators, remove duplicates and identity elements, and test whether elm is already contained in G.

This functions returns the closure of the group G with the element elm. If G has the attribute AsSSortedList then also the result has this attribute. This is used to implement the default method for Enumerator (see Enumerator) and EnumeratorSorted (see EnumeratorSorted).

For a group G that stores a parent group (see Parents), ClosureSubgroup calls ClosureGroup (see ClosureGroup) with the same arguments; if the result is a subgroup of the parent of G then the parent of G is set as parent of the result, otherwise an error is raised. The check whether the result is contained in the parent of G is omitted by the NC version.

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