Algorithms for continuous and discrete abelian groups and their related classes

In this paper, algorithms are developed to determine properties of finite Z-modules (i.e., abelian groups) related to the classes of (quasi)continuous and (quasi)discrete groups. To this end, some algorithms are provided to check whether the groups have the summand intersection (sum) property, generalized summand intersection (sum) property or absolute direct summand property, and to check whether the groups are virtually semisimple, virtually C2, virtually extending, C2, C3, D2, D3, (quasi)continuous or (quasi)discrete. The algorithms are implemented and published as a collection of GAP4 functions named <b>codiaga</b> (see [22]).