Research Article
Year 2021,
Volume: 30 Issue: 30, 66 - 77, 17.07.2021
Abstract
References
- J. Aczel and J. Dhombres, Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications, 31, Cambridge University Press, Cambridge, 1989.
- G. M. Bergman, A note on factorizations of finite groups, J. Iran. Math. Soc., 1(2) (2020), 157-161.
- A. H. Clifford and D. D. Miller, Semigroups having zeroid elements, Amer. J. Math., 70(1) (1948), 117-125.
- K. Corradi and S. Szabo, Factoring certain infinite abelian groups by cyclic subsets, Pure Math. Appl. Ser. A, 2 (1992), 285-290.
- G. Hajos, Uber einfache und mehrfache Bedeckung des $n$-dimensionalen Raumes mit einem Wurfelgitter, Math. Z., 47 (1941), 427-467.
- M. H. Hooshmand, Grouplikes, Bull. Iranian Math. Soc., 39(1) (2013), 65-85.
- M. H. Hooshmand, New results for the multiplicative symmetric equation and related conjecture, Aequationes Math., 94(1) (2020), 123-136.
- R. P. Hunter, On the structure of homogroups with applications to the theory of compact connected semigroups, Fund. Math., 52 (1963), 69-102.
- A. D. Sands, The factorization of abelian groups II, Quart. J. Math. Oxford Ser. (2), 13 (1962), 45-54.
- S. Schwarz, Semigroups with a universally minimal left ideal, Acta Sci. Math. (Szeged), 52(1-2) (1988), 21-28.
- S. Szabo and A. D. Sands, Factoring Groups Into Subsets, Lecture Notes in Pure and Applied Mathematics, 257, CRC Press, Boca Raton, FL, 2009.
Year 2021,
Volume: 30 Issue: 30, 66 - 77, 17.07.2021
Abstract
The $b$-parts, $b$-addition of real numbers and some of their
extensions (e.g., $f$-multiplications) were introduced and studied
by the author. In this paper, we introduce $f$-representatives
groups of a given group $(G,\cdot)$ which can be considered as a
generalization of the group of the least non-negative residues
(modulo $n$). Thereafter, we study some of their important
properties and their relations among the ground group $(G,\cdot)$,
a related quotient group, and $f$-grouplikes. Finally, many
equivalent conditions for $f$-representatives groups and several
examples in the group of real numbers are given.
References
- J. Aczel and J. Dhombres, Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications, 31, Cambridge University Press, Cambridge, 1989.
- G. M. Bergman, A note on factorizations of finite groups, J. Iran. Math. Soc., 1(2) (2020), 157-161.
- A. H. Clifford and D. D. Miller, Semigroups having zeroid elements, Amer. J. Math., 70(1) (1948), 117-125.
- K. Corradi and S. Szabo, Factoring certain infinite abelian groups by cyclic subsets, Pure Math. Appl. Ser. A, 2 (1992), 285-290.
- G. Hajos, Uber einfache und mehrfache Bedeckung des $n$-dimensionalen Raumes mit einem Wurfelgitter, Math. Z., 47 (1941), 427-467.
- M. H. Hooshmand, Grouplikes, Bull. Iranian Math. Soc., 39(1) (2013), 65-85.
- M. H. Hooshmand, New results for the multiplicative symmetric equation and related conjecture, Aequationes Math., 94(1) (2020), 123-136.
- R. P. Hunter, On the structure of homogroups with applications to the theory of compact connected semigroups, Fund. Math., 52 (1963), 69-102.
- A. D. Sands, The factorization of abelian groups II, Quart. J. Math. Oxford Ser. (2), 13 (1962), 45-54.
- S. Schwarz, Semigroups with a universally minimal left ideal, Acta Sci. Math. (Szeged), 52(1-2) (1988), 21-28.
- S. Szabo and A. D. Sands, Factoring Groups Into Subsets, Lecture Notes in Pure and Applied Mathematics, 257, CRC Press, Boca Raton, FL, 2009.
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | July 17, 2021 |
| Published in Issue | Year 2021 Volume: 30 Issue: 30 |