A generalized Goursat lemma

Kristine Bauer 1 , Debasis Sen 2 , and Peter Zvengrowski 1
  • 1 Department of Mathematics and Statistics University of Calgary Calgary, Alberta CANADA T2N 1N4
  • 2 Department of Mathematics and Statistics Indian Institute of Technology Kanpur INDIA


In this note the usual Goursat lemma, which describes subgroups of the direct product of two groups, is generalized to describing subgroups of a direct product A1 × A2 × · · · × An of a finite number of groups. Other possible generalizations are discussed and applications characterizing several types of subgroups are given. Most of these applications are straightforward, while somewhat deeper applications occur in the case of profinite groups, cyclic groups, and the Sylow p-subgroups (including infinite groups that are virtual p-groups).

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