Abstract
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.
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Brewster, B., Lewis, D. A characterization of subgroup containment in direct products. Ricerche mat. 61, 347–354 (2012). https://doi.org/10.1007/s11587-012-0135-3
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DOI: https://doi.org/10.1007/s11587-012-0135-3