Original Article

Ricerche di Matematica

, Volume 61, Issue 2, pp 347-354

First online:

A characterization of subgroup containment in direct products

  • Ben BrewsterAffiliated withDepartment of Mathematical Sciences, Binghamton University
  • , Dandrielle LewisAffiliated withDepartment of Mathematics, University of Wisconsin-Eau Claire Email author 

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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 subgroups Lattices of subgroups Extraspecial groups Direct products P-groups

Mathematics Subject Classification (2000)

20D40 20E15