Euler's totient function applied to complete hypergroups

Author:

Sonea Andromeda1,Cristea Irina2

Affiliation:

1. Department of Science, University of Life Sciences, Iaşi, Romania

2. Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, Nova Gorica 5000, Slovenia

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference23 articles.

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2. J. Mittas, Hypergroupes canoniques, Math. Balkanica, 2 (1972), 165–179.

3. K. Kuhlmann, A. Linzi, H. Stojalowska, Orderings and valuations in hyperfields, J. Algebra, 611 (2022), 399–421. https://doi.org/10.1016/j.jalgebra.2022.08.006

4. A. Linzi, H. Stojałowska, Hypervaluations on hyperfields and ordered canonical hypergroups, Iran. J. Math. Sci. Inf., In press.

5. P. Bonansinga, Quasicanonical hypergroups, Atti Soc. Peloritana Sci. Fis. Mat. Natur., 27 (1981), 9–17.

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