Brewster, B. & Lewis, D. Ricerche mat. (2012) 61: 347. doi:10.1007/s11587-012-0135-3
Using Goursat’s characterization of subgroups in a direct product, a characterization of subgroup containment in such a direct product is given. Applying this along with facts about p-groups we describe a process for obtaining the subgroup lattice of a direct product of p-groups. This process is implemented to portray the subgroup lattice of Q × Q, where Q is the quaternion group of order 8.
Products of subgroupsLattices of subgroupsExtraspecial groupsDirect productsP-groups