Some applications of group theoretical programs

Abstract

Both special purpose programs and more general systems have been implemented for the study of groups. The special programs were in most cases designed for calculations occurring in the investigation of very big finite groups, such as some of the newly discovered simple groups. The general systems in most cases allow a fairly detailed analysis of comparatively small groups only. Of course, general systems can be used to construct examples for teaching and for testing hypotheses, but often the more detailed structure of smaller subgroups of big groups, e.g., their Sylow subgroups, is needed. Another application of such a system, namely, to the classification of crystallographic groups and lattices in 4-dimensional space will be emphasized.