The order of the group G, returned as an ordinary integer. If G is an infinite group, the value zero is returned.
The factored order of the group G, returned as a sequence of prime-exponent pairs. If G is an infinite group, the empty sequence is returned.
The index of the subgroup H in the group G, returned as an ordinary integer. If H has infinite index in G, the value zero is returned.
The factored index of the subgroup H in the group G, returned as a sequence of prime-exponent pairs. If H has infinite index in G, the empty sequence is returned.
The exponent of the group G. If the group is infinite, the value zero is returned.
True if the group G is finite.
g in G : GrpAbElt, GrpAb -> BoolElt
Given an element g and a group G, return true if g is an element of G, false otherwise.
Given an element g and a group G, return true if g is not an element of G, false otherwise.
Given an group G and a set S of elements belonging to a group H, where G and H have some covering group, return true if S is a subset of G, false otherwise.
Given a group G and a set S of elements belonging to a group H, where G and H have some covering group, return true if S is not a subset of G, false otherwise.
Given groups G and H, subgroups of some common overgroup, return true if H is a subgroup of G, and false otherwise.
Given groups G and H, subgroups of some common overgroup, return true if H is not a subgroup of G, and false otherwise.
Given groups G and H, subgroups of some common overgroup, return true if G and H are identical, and false otherwise.
Given groups G and H, subgroups of some common overgroup, return true if G and H are distinct groups, and false otherwise.
A bijective mapping from the finite group G onto the set of integers { 1 ... |G| }. The actual mapping depends upon choice of standard generators for G.
An element chosen at random from the group G.
Slots: RngIntElt Default: 10
Scramble: RngIntElt Default: 100
Create a process to generate randomly chosen elements from the abelian group G. The process uses an `expansion' procedure to construct a set of elements corresponding to fairly long words in the generators of G. At all times, N elements are stored where N is the maximum of n and Ngens(G) + 1. Initially, these are just the generators of G and products of pairs of generators of G. Random elements are now produced by successive calls to Random(P), where P is the process created by this function. Each such call chooses an element from the process and returns it, replacing it with the product of it and another random element (on the left or the right). The Scramble parameter causes m such operations to be performed before the process is returned.
Given a random element process P for the abelian group G created by the function RandomProcess(G), construct a random element of G by forming a random product over the expanded generating set stored as part of the process. The expanded generating set stored with the process is modified by replacing an existing generator by the element returned.
A representative element of G.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]