PERMUTATION GROUPS IN MAGMA

Аннотация

Groups arise in several different categories in Magma. In the case of the category of permutation groups and the category of soluble groups defined by a power-conjugate presentation, all groups in the category are finite. However, the finitely-presented group category, the polycyclic group category, the abelian group category and the matrix group category contain both finite and infinite groups. In the case of the abelian group category and the matrix group category, a large number of functions are available for finite groups only. In the near future, these functions will be extended to finite finitely-presented groups of moderate order. In this paper we discuss the group of permutations , solve some problems that are only available for finite groups.