Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.25972 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909816587288576 |
|---|---|
| author | Calero-Sanz, Jorge Prieto-Martínez, Luis Felipe |
| author_facet | Calero-Sanz, Jorge Prieto-Martínez, Luis Felipe |
| contents | We investigate the existence and uniqueness of iterative roots of order $n$ within the substitution group of formal power series $\mathcal J(Z)$ -- with coefficients in a commutative ring with unity $Z$ -- employing a matrix-based framework grounded in the Riordan group. We analyse the relationship between the substitution group and the Lagrange subgroup -- a group of Riordan matrices -- and explore some classic questions concerning algebraic completeness and uniqueness of root extractions. This approach allows us to obtain various results about the roots in $\mathcal J(Z)$ for different choices of $Z$. Furthermore, the examination of the substitution group facilitates the analysis of roots within the Riordan matrix group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Roots in the substitution group and in the group of Riordan matrices with ones in the main diagonal Calero-Sanz, Jorge Prieto-Martínez, Luis Felipe Group Theory 13F25, 13J05, 15A99, 16W60 We investigate the existence and uniqueness of iterative roots of order $n$ within the substitution group of formal power series $\mathcal J(Z)$ -- with coefficients in a commutative ring with unity $Z$ -- employing a matrix-based framework grounded in the Riordan group. We analyse the relationship between the substitution group and the Lagrange subgroup -- a group of Riordan matrices -- and explore some classic questions concerning algebraic completeness and uniqueness of root extractions. This approach allows us to obtain various results about the roots in $\mathcal J(Z)$ for different choices of $Z$. Furthermore, the examination of the substitution group facilitates the analysis of roots within the Riordan matrix group. |
| title | Roots in the substitution group and in the group of Riordan matrices with ones in the main diagonal |
| topic | Group Theory 13F25, 13J05, 15A99, 16W60 |
| url | https://arxiv.org/abs/2509.25972 |