Computing and Visualizing Lattices of Subgroups Using Relation Algebra and RelView

Abstract

We model groups as relational systems and develop relation-algebraic specifications for direct products of groups, quotient groups, and the enumeration of all subgroups and normal subgroups. The latter two specifications immediately lead to specifications of the lattices of subgroups and normal subgroups, respectively. All specifications are algorithmic and can directly be translated into the language of the computer system RelView. Hence, the system can be used for constructing groups and for computing and visualizing their lattices of subgroups and normal subgroups. This is demonstrated by some examples.KeywordsNormal SubgroupMaximal SubgroupQuotient GroupNeutral PointNeutral ElementThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.