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Substitution groups of formal power series
Abstract
Let G be the group of power series x+a2x2+a3x3+⋯∈ R[[x]] under substitution, where R is a commutative ring with 1≠ 0 of prime characteristic p. Given any n≥ 1, the subgroup Kn={x+an+1xn+1+an+2xn+2+⋯ | ai∈ R} is normal in G, and the quotient Gn=G/Kn is the group of truncated polynomials over R of degree ≤ n under substitution. In this paper, we compute the exponent of the image of Kr in Gn, for all r,n≥ 1, indicating in every case a family of elements realizing this exponent.
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BibTeX
@misc{dalessandro2026substitution,
title = {{Substitution groups of formal power series}},
author = {Agustín D'Alessandro and Fernando Szechtman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.11461},
eprint = {2606.11461},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.11461},
}
RIS
TY - UNPB
TI - Substitution groups of formal power series
AU - Agustín D'Alessandro
AU - Fernando Szechtman
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.11461
UR - https://arxiv.org/abs/2606.11461
AB - Let G be the group of power series x+a_2x^2+a_3x^3+⋯∈ R[[x]] under substitution, where R is a commutative ring with 1≠ 0 of prime characteristic p. Given any n≥ 1, the subgroup K_n={x+a_n+1x^n+1+a_n+2x^n+2+⋯ | a_i∈ R} is normal in G, and the quotient G_n=G/K_n is the group of truncated polynomials over R of degree ≤ n under substitution. In this paper, we compute the exponent of the image of K_r in G_n, for all r,n≥ 1, indicating in every case a family of elements realizing this exponent.
ER -