<abstract xmlns="http://www.w3.org/1999/xhtml"> 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).</abstract>

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).

A generalized Goursat lemma

Department of Mathematics and Statistics University of Calgary Calgary, Alberta CANADA T2N 1N4

Department of Mathematics and Statistics Indian Institute of Technology Kanpur INDIA

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A generalized Goursat lemma"}

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...

A generalized Goursat lemma

Online veröffentlicht: 19. Feb. 2016

Seitenbereich: 1 - 19

Eingereicht: 02. Nov. 2015

DOI: https://doi.org/10.1515/tmmp-2015-0039

Schlüsselwörter
Goursat’s lemma.

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A generalized Goursat lemma

Online veröffentlicht: 19. Feb. 2016

Seitenbereich: 1 - 19

Eingereicht: 02. Nov. 2015

DOI: https://doi.org/10.1515/tmmp-2015-0039

SchlüsselwörterGoursat’s lemma.

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
Goursat’s lemma.