Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers

Beshimov, Gayrat

O‘zbekiston matematika jurnali · 2025-yil

Annotatsiya

Let $Q$ be the field of rational numbers and $Q^{2}$ be the $2$-dimensional linear space over $Q$. A classification of all non-degenerate symmetric bilinear-metric forms over $Q^{2}$ have obtained. Let $\varphi $ be a non-degenerate symmetric bilinear form on $Q^{2}$. Denote by $O(2,\varphi, Q)$ the group of all $\varphi$-orthogonal (that is the form $\varphi$ preserving) transformations of $Q^{2}$. Put $MO( 2,\varphi, Q)=\left\{F:Q^{2}\rightarrow Q^{2}\mid Fx=gx+b, g\in O(2,\varphi, Q), b\in Q^{2}\right\}$, $SO(2,\varphi, Q)=\left\{ g\in O(2, \varphi, Q)|detg=1\right\}$ and $MSO(2, \varphi, Q)= \left\{F\in M(2, \varphi, Q)|detg=1\right\}$.The present paper is devoted to solutions of problems of $G$-equivalence of $m$-tuples in $Q^{2}$ for groups $G=O(2,\varphi, Q), SO(2,\varphi, Q)$, $MO(2,\varphi, Q)$, $MSO(2,\varphi, Q)$. Complete systems of $G$-invariants of $m$-tuples in $Q^{2}$ for these groups are obtained.

Maqola ma’lumotlari
MualliflarBeshimov, Gayrat
JurnalO‘zbekiston matematika jurnali
NashriyotЎзбекистон Республикаси ФА Математика институти
ISSN2010-7269
Nashr sanasi2025-11-03
Jild69
Son4
Betlar53-69
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.29229/uzmj.2025-4-7
Indeksga qo‘shilgan2026-08-26

DOI: 10.29229/uzmj.2025-4-7 · Maqolaning asl sahifasi

Kalit so‘zlar

Invariant of $m$-tuple; $m$-point invariant.

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APABeshimov, Gayrat (2025). Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers. O‘zbekiston matematika jurnali, 69(4), 53-69. https://doi.org/10.29229/uzmj.2025-4-7
GOST (OAK)Beshimov, Gayrat Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 53-69. – DOI: 10.29229/uzmj.2025-4-7.
MLABeshimov, Gayrat. “Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers.” O‘zbekiston matematika jurnali, 69(4), 53-69, 2025. https://doi.org/10.29229/uzmj.2025-4-7
ChicagoBeshimov, Gayrat. “Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers.” O‘zbekiston matematika jurnali, 69(4), 53-69 (2025). https://doi.org/10.29229/uzmj.2025-4-7
HarvardBeshimov, Gayrat (2025) ‘Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers’, O‘zbekiston matematika jurnali, 69(4), 53-69. https://doi.org/10.29229/uzmj.2025-4-7
BibTeX
@article{beshimovgayrat2025,
  title = {Complete systems of invariants of $m$-tuples for fundamental groups of a two-dimensional bilinear-metric space over the field of rational numbers},
  author = {Beshimov, Gayrat},
  journal = {O‘zbekiston matematika jurnali},
  year = {2025},
  volume = {69},
  number = {4},
  pages = {53-69},
  doi = {10.29229/uzmj.2025-4-7},
  url = {https://doi.org/10.29229/uzmj.2025-4-7}
}

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