Let $E_{2}$ be the $2$-dimensional Euclidean space and $T$ be a set such that it has at least two elements. A mapping $\alpha : T\rightarrow E_{2}$ will be called a $T$-figure in $E_{2}$. Let $O(2, R)$ be the group of all orthogonal transformations of $E_{2}$. Put $SO(2, R)=\left\{ g\in O(2, R)|detg=1\right\}$, $MO(2, R)=\left\{F:E_{2}\rightarrow E_{2}\mid Fx=gx+b, g\in O(2,R), b\in E_{2}\right\}$,
$MSO(2, R)= \left\{F\in MO(2, R)|detg=1\right\}$.
The present paper is devoted to solutions of problems of $G$-equivalence of $T$-figures in $E_{2}$ for groups $G=O(2, R), SO(2, R)$, $MO(2, R)$, $MSO(2, R)$. Complete systems of $G$-invariants of $T$-figures in $E_{2}$ for these groups are obtained. Complete systems of relations between elements of the obtained complete systems of $G$-invariants are given for these groups.
The Ministry of Innovative Development of the Republic of Uzbekistan and The Scientific and Technological Research Council of Turkey
UT-OT-2020-2 and 119N643
This work is supported by The Ministry of Innovative Development of the Republic of Uzbekistan (MID Uzbekistan) under Grant Number UT-OT-2020-2 and The Scientific and Technological Research Council of Turkey (T\"{U}B{\.I}TAK) under Grant Number 119N643.
UT-OT-2020-2 and 119N643
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Proje Numarası | UT-OT-2020-2 and 119N643 |
Yayımlanma Tarihi | 30 Mart 2023 |
Gönderilme Tarihi | 3 Ekim 2021 |
Kabul Tarihi | 19 Eylül 2022 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 72 Sayı: 1 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.