The algebra of crystallographic groups in dimension two
| Autor: | Manuel R. F. Moreira |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Algebra and Its Applications. 21 |
| ISSN: | 1793-6829 0219-4988 |
| Popis: | Starting with the two semi-direct products of two copies of the group of integers, a description of all possible semi-direct products of these two groups with finite groups, under a faithful action, is obtained. The results are groups that are isomorphic to 16 crystallographic groups in dimension two. An extra effort gives us a group isomorphic to the 17th crystallographic group. Four of the crystallographic groups are shown to be the only solutions to a natural generalization of the semi-direct product of two copies of the group of integers. Finally, we verify that the two additional groups, that are solution to the generalization of the semi-direct product of two copies of the integers, preserve stability in the sense that their semi-direct products with finite groups under a faithful action give rise only to crystallographic groups, if we disregard some trivial outcomes. |
| Databáze: | OpenAIRE |
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