On Non-perfect Colorings Arising from Index 4 Subgroups

Authors

Rene P. Felix, University of the Philippines Diliman
Ma. Louise Antonette N. De Las Peñas, Ateneo de Manila UniversityFollow

Document Type

Article

Publication Date

2003

Abstract

For a non-perfect coloring corresponding to the decomposition of the form G = U^t_i=1 U_hεHhJ_iY_i of the symmetry group G of an uncolored pattern, where J₁, H, K are subgroups of G such that K ≤ J_i ≤ H ≤ N_G(K) and Y = U^t_i=1 Y_i 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.

Recommended Citation

Felix, R. P., & De Las Peñas, M. (2003). On Non-Perfect Colorings Arising from Index 4 Subgroups. Southeast Asian Bulletin of Mathematics, 27(4).