Introduction to D[subscript]8 x D[subscript]8 and its Subgroup Lattice

Abstract

Let A and B be groups and consider the direct product A x B. In regards to subgroups A x B, in 1889, Edouard Goursat proved a theorem that provides the structure of subgroups in a direct product. This study applied the subgroup containment theorem, which uses the same notation as Goursat's Theorem, to the specific case of D[subscript]8 x D [subscript]8. The intention of this study is to improve and make more effective this containment theorem for further use.