Group covers with a specified pairwise intersection
Andrew Penland · NC Digital Online Collection of Knowledge and Scholarship (The University of North Carolina at Greensboro) · 2011
A collection of subgroups whose union is equal to the whole group is known as a group cover. Various types of group covers have been explored in recent years. In this work, we define a new type of cover, an equal L-intersection cover, which is specified by the size and pairwise intersection of the subgroups involved. We demonstrate that this cover is in fact distinct from previous classes of group covers. Further, we give tests to determine whether or not a finite group has this type of cover. These tests are implemented in the computational algebra program GAP to find new instances of equal L-intersection covers. These examples lead to interesting questions and conjectures.