SUBGROUP LATTICE ALGORITHMS RELATED TO EXTENDING AND LIFTING ABELIAN GROUPS

Abstract

We develop algorithms for determining properties of finite abelian groups related to the notions of extending and lifting groups. Thus, we give efficient methods, on one hand to check the properties of being direct summand, essential, superfluous, coessential, complement (closed), supplement (coclosed) subgroup, and on the other hand to determine all subgroups with the mentioned properties of a given finite abelian group.