The functions in this group provide access to basic information stored for a group G.
The i-th defining generator for G, if i>0. If i<0, then the inverse of the -i-th defining generator is returned. G.0 is equivalent to Identity(G).
A set containing the defining generators for G.
The number of defining generators for G.
Given a group G in the category GrpPerm or GrpMat, return the generic group containing G, i.e., the largest group in which G is naturally embedded. The precise definition of generic group depends upon the category to which G belongs.
The parent group G for the group element g.
> K<z> := GF(2, 3); > G := SuzukiGroup(8); > Generic(G); GL(4, GF(2, 3)) > Ngens(G); 3 > for i in [1..3] do > print "generator", i, G.i; > print "order", Order(G.i), "\r"; > end for; generator 1 [ 0 0 0 1] [ 0 0 1 0] [ 0 1 0 0] [ 1 0 0 0] order 2 generator 2 [z^2 0 0 0] [ 0 z^6 0 0] [ 0 0 z 0] [ 0 0 0 z^5] order 7 generator 3 [ 1 0 0 0] [z^2 1 0 0] [ 0 z 1 0] [z^5 z^3 z^2 1] order 4
Given a finitely generated group G that acts on the parent structure of x through the map (or user defined function) M, compute the orbit of x under G. Thus, for every generator g of G, M(g) must return a function that can be applied to x or any other element in the parent of x.If the orbit is infinite, this process will eventually run out of memory.
Given a finitely generated group G acting on the universe of S through the map or user defined function M, compute the smallest subset T containing S that is G-invariant. Thus, for every generator g of G, M(g) must return a function that can be applied to an arbitrary element in the universe of S.[Next][Prev] [Right] [Left] [Up] [Index] [Root]If the orbit closure is infinite, this process will eventually run out of memory.