42.17 Conjugacy Classes in Solvable Groups

computes conjugacy classes and centralizers in solvable groups. G is the acting group. mode indicates the type of the calculation:

0 Conjugacy classes

4 Conjugacy test for the two elements in opt.candidates

In mode 0 the function returns a list of records containing components representative and centralizer. In mode 4 it returns a conjugating element.

The optional record opt may contain the following components that will affect the algorithms behaviour:

pcgs

is a pcgs that will be used for the calculation. In the case of the calculation of rational classes, it must be a pcgs refining a central series. The attribute NormalSeriesByPcgs must return an appropriate series of normal subgroups with elementary abelian factors among them. The algorithm will step down this series. By default an ElementaryAbelianSeries is used.

candidates

is a list of elements for which canonical representatives are to be computed or for which a conjugacy test is performed. They must be given in mode 4. In mode 0 a list of classes corresponding to candidates is returned (which may contain duplicates). The representatives chosen are canonical with respect to pcgs. The records returned also contain components operator such that (candidate ^ operator) =representative.

See also SubgroupsSolvableGroup. [Top] [Previous] [Up] [Index]