On Non-perfect Colorings Arising from Index 4 Subgroups

• Main Authors: Felix, Rene P, De Las Peñas, Ma. Louise Antonette N
• Format: text
• Published: Archīum Ateneo 2003
• Subjects: Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/113; https://web.b.ebscohost.com/abstract?direct=true&profile=ehost&scope=site&authtype=crawler&jrnl=01292021&asa=Y&AN=13075772&h=AKY7YTaIdEVS%2fDgihHeIxsiVTE%2fDK3IEyaX%2fM7m5kv0N%2bjvs1gBO%2bnTgT42VoHG06p%2fu0mXT20ceJzK%2b64lZFw%3d%3d&crl=c&resultNs=AdminWebAuth&resultLocal=ErrCrlNotAuth&crlhashurl=login.aspx%3fdirect%3dtrue%26profile%3dehost%26scope%3dsite%26authtype%3dcrawler%26jrnl%3d01292021%26asa%3dY%26AN%3d13075772
• Institution: Ateneo De Manila University

For a non-perfect coloring corresponding to the decomposition of the form G = Uti=1 UhεHhJiYi of the symmetry group G of an uncolored pattern, where J1, H, K are subgroups of G such that K ≤ Ji ≤ H ≤ NG(K) and Y = Uti=1 Yi a complete set of right coset representatives of H in G where [G : H] = 4, we determine formulas for the subgroups H* and K* consisting of elements of G permuting and fixing the colors respectively. The techniques developed in this paper provide the direction in determining H* and K* for the cases where the index of H in G is a composite bigger that 4.