2013/06/18 by Gary L. Walls, Gary Walls, Linhong Wang +2
Engineering · Mathematics · #16S60 #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #graph theory and CDMA systems #math.RA #msc:16S60
paper · pdf · doi:10.48550/arxiv.1306.4286
11 pages. No figures. To appear Turkish Journal of Mathematics
openalex publication_date 2013/06/18 · arxiv created 2016/02/23 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when restricted to the elements of a cover of the group by abelian subgroups. We give an algorithm which allows us to determine the elements of the ring of functions of a finite p-group which arises in this manner when the elements of the cover are required to be either cyclic or elementary abelian of rank 2. This enables us to determine the actual structure of such a ring as a subdirect product. A key part of the argument is the construction of a graph whose vertices are the subgroups of order p and whose edges are determined by the covering.