Orbits of $\QQ^*(\sqrt{n})$ under the action of Modular Group $PSL(2,\mathbb {Z})$

Details Orbits of $\QQ^*(\sqrt{n})$ under the action of Modular Group $PSL(2,\mathbb {Z})$ Orbits of $\QQ^*(\sqrt{n})$ under the action of Modular Group $PSL(2,\mathbb {Z})$

2011-04-04

arxiv.org/abs/1104.0515v3

Mathematics

Group Theory

This paper includes 10 pages and 16 references

Scientific paper

Coset diagrams have been used to study quotients, orbits, subgroups and structure of the finitely generated groups. In this paper we use coset diagrams and modular arithmetic to determine the $G$-orbits of $\QQ^*(\sqrt{p^k})$, $\QQ^*(\sqrt{2p^k})$, $\QQ^*(\sqrt{2^2p^k})$, and in general $\QQ^*(\sqrt{2^lp^k})$, for each $l\geq3$ and $k=2h+1\geq3$, for each odd prime $p$.

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