Euler's totient function applied to complete hypergroups
We study the Euler's totient function (called also the Euler's phi function) in the framework of finite complete hypergroups. These are algebraic hypercompositional structures constructed with the help of groups, and endowed with a multivalued operation, called hyperoperation. On them the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023388?viewType=HTML |
| _version_ | 1811170984945778688 |
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| author | Andromeda Sonea Irina Cristea |
| author_facet | Andromeda Sonea Irina Cristea |
| author_sort | Andromeda Sonea |
| collection | DOAJ |
| description | We study the Euler's totient function (called also the Euler's phi function) in the framework of finite complete hypergroups. These are algebraic hypercompositional structures constructed with the help of groups, and endowed with a multivalued operation, called hyperoperation. On them the Euler's phi function is multiplicative and not injective. In the second part of the article we find a relationship between the subhypergroups of a complete hypergroup and the subgroups of the group involved in the construction of the considered complete hypergroup. As sample application of this connection, we state a formula that relates the Euler's totient function defined on a complete hypergroup to the same function applied to its subhypergroups. |
| first_indexed | 2024-04-10T17:07:03Z |
| format | Article |
| id | doaj.art-24d9c5363abb4b07ac8b175657e7efcb |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T17:07:03Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-24d9c5363abb4b07ac8b175657e7efcb2023-02-06T02:11:09ZengAIMS PressAIMS Mathematics2473-69882023-01-01847731774610.3934/math.2023388Euler's totient function applied to complete hypergroupsAndromeda Sonea0Irina Cristea 11. Department of Science, University of Life Sciences, Iaşi, Romania2. Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, Nova Gorica 5000, SloveniaWe study the Euler's totient function (called also the Euler's phi function) in the framework of finite complete hypergroups. These are algebraic hypercompositional structures constructed with the help of groups, and endowed with a multivalued operation, called hyperoperation. On them the Euler's phi function is multiplicative and not injective. In the second part of the article we find a relationship between the subhypergroups of a complete hypergroup and the subgroups of the group involved in the construction of the considered complete hypergroup. As sample application of this connection, we state a formula that relates the Euler's totient function defined on a complete hypergroup to the same function applied to its subhypergroups.https://www.aimspress.com/article/doi/10.3934/math.2023388?viewType=HTMLeuler's totient functioncomplete hypergroupperiod of an elementheart of a hypergroup |
| spellingShingle | Andromeda Sonea Irina Cristea Euler's totient function applied to complete hypergroups AIMS Mathematics euler's totient function complete hypergroup period of an element heart of a hypergroup |
| title | Euler's totient function applied to complete hypergroups |
| title_full | Euler's totient function applied to complete hypergroups |
| title_fullStr | Euler's totient function applied to complete hypergroups |
| title_full_unstemmed | Euler's totient function applied to complete hypergroups |
| title_short | Euler's totient function applied to complete hypergroups |
| title_sort | euler s totient function applied to complete hypergroups |
| topic | euler's totient function complete hypergroup period of an element heart of a hypergroup |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023388?viewType=HTML |
| work_keys_str_mv | AT andromedasonea eulerstotientfunctionappliedtocompletehypergroups AT irinacristea eulerstotientfunctionappliedtocompletehypergroups |