ABOUT COMPUTER TECHNOLOGIES IN THE STUDY OF SUBSTITUTION GROUPS

The article discusses the features of using the Maple package of mathematical symbolic calculations in the study of substitution groups, which are important objects of the courses «Discrete Mathematics», «Algebra» and «Algebra and Geometry». The paper demonstrates a technique for using the «Group Theory» subpackage to verify whether a given group is Abelian, metabelian, solvable, or nilpotent. At the same time, an illustration of the Sylow theorem on the number of Sylow subgroups and their conjugacy appears. The subgroup participating in the experiment is defined by random generating elements, and therefore the student of the course can repeatedly conduct such computer-group experiments himself, simply returning to the beginning of the program.