Ricerche di Matematica

, Volume 61, Issue 2, pp 347–354

A characterization of subgroup containment in direct products

Original Article

DOI: 10.1007/s11587-012-0135-3

Cite this article as:
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 subgroups Lattices of subgroups Extraspecial groups Direct products P-groups 

Mathematics Subject Classification (2000)

20D40 20E15 

Copyright information

© Università degli Studi di Napoli "Federico II" 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesBinghamton UniversityBinghamtonUSA
  2. 2.Department of MathematicsUniversity of Wisconsin-Eau ClaireEau ClaireUSA

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