36.15 Numerical Group Attributes

Computes the abelian invariants of the commutator factor group of G. They are given as a list of the orders of a set of independent generators of G/G¢ (see IndependentGeneratorsOfAbelianGroup).

gap> g:=Group((1,2,3,4),(1,2),(5,6));;
gap> AbelianInvariants(g);
[ 2, 2 ]

The exponent e of a group G is the lcm of the orders of its elements, that is, e is the smallest integer such that g^e = 1 for all g Î G

gap> Exponent(g);
12

Again the following are mathematical attributes, but not GAP Attributes as they are depending on a parameter:

returns the number of n-tuples (g₁, g₂, ¼g_n) of elements of the group G that generate the whole group G. The elements of an n-tuple need not be different.

gap> EulerianFunction(g,2);
432

[Top] [Previous] [Up] [Next] [Index]