Subgroups of 3-factor direct products

Rok, strany: 2019, 19 - 38

Extending Goursat's Lemma we investigate the structure of subdirect products of 3-factor direct products. We construct several examples and then provide a structure theorem showing that every such group is essentially obtained by a combination of the examples. The central observation in this structure theorem is that the dependencies among the group elements in the subdirect product that involve all three factors are of Abelian nature. In the spirit of Goursat's Lemma, for two special cases, we derive correspondence theorems between data obtained from the subgroup lattices of the three factors (as well as isomorphisms between arising factor groups) and the subdirect products. Using our results we derive an explicit formula to count the number of subdirect products of the direct product of three symmetric groups.

ISO 690:

Neuen, D., Schweitzer, P. 2019. Subgroups of 3-factor direct products. In Tatra Mountains Mathematical Publications, vol. 73, no.1, pp. 19-38. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0003

APA:

Neuen, D., Schweitzer, P. (2019). Subgroups of 3-factor direct products. Tatra Mountains Mathematical Publications, 73(1), 19-38. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0003

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

© 2019 Mathematical Institute, Slovak Academy of Sciences. Licensed under the Creative Commons Attribution-NC-ND 4.0 International Public License.