minimal-groups
Science Score: 54.0%
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Low similarity (7.0%) to scientific vocabulary
Repository
Basic Info
- Host: GitHub
- Owner: HDaniels432
- License: mit
- Language: MATLAB
- Default Branch: main
- Size: 2.49 MB
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- Stars: 0
- Watchers: 1
- Forks: 0
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Metadata Files
README.md
This repository hosts code and data related to the paper titled Minimal Subgroups of GL2(ZS) by Harris B. Daniels and Jeremy Rouse, arXiv:2402.11049 (2024).
The directory structure is organized as follows:
Ancestor: This directory contains Magma code for computing the labels of all supergroups of a given subgroup of GL2(Z2).
Aux Files: Here you will find Magma code and data sourced from other papers used in our computations. Specifically, it includes:
gl2.m
gl2data.m
gl2_big2adic
These files originate from ell-adic images of Galois for elliptic curves over Q by Jeremy Rouse, Andrew V. Sutherland, and David Zureick-Brown, cited as [15] in our paper.
Minimal Group Search: The subdirectory Found Groups contains scripts dedicated to identifying minimal groups at various levels that are powers of 2. The file minsearch.txt is a Magma script that, given a positive integer n, finds subgroups of GL2(Z/2n Z) whose full preimage in GL2(Z2) is minimal. This script was run for n = 3 to n = 7 and the outputs are in the files minfound3.txt, minfound4.txt, …, minfound7.txt. (The file minfoundn.txt is formatted as a Magma script the specifies a tuple “subs” consisting of all of the minimal groups of level <= 2n.)
The folder Logs houses the corresponding log files from these searches. The file Genus0MinimalGroups.m includes the Magma code needed to compute the models of the genus 0 minimal groups that appear in Section 5 of the paper.
Plentiful: This directory holds the code which does the calculation mentioned in the final paragraph of the proof of Theorem 4.2. In particular, it shows that for each pair (A,B) of matrices in GL2(Z/4Z)2, the power series d defined in the paper is nonzero.
Owner
- Login: HDaniels432
- Kind: user
- Repositories: 1
- Profile: https://github.com/HDaniels432
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!
cff-version: 1.2.0
title: Minimal Subgroups of GL_2(Z_S)
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
authors:
- given-names: Harris
family-names: Daniels
email: hdaniels@amherst.edu
affiliation: Amherst College
- given-names: Jeremy
family-names: Rouse
email: rouseja@wfu.edu
affiliation: Wake Forest University
license: MIT