[Merged by Bors] - feat(GroupTheory/IndexNSmul): add results on multiplication-by-n in AddCommGroups

[MichaelStollBayreuth]

This PR adds a new file (to be able to have the required imports) that contains some results related to the (relative) index of subgroups in commutative additive groups and the multiplication-by-n map.

They will be useful in proving the Northcott property for heights on number fields.

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• depends on: [Merged by Bors] - feat(Algebra/Group): some API lemmas for powMonoidHom #36458 [some API lemmas for powMonoidHom]

[github-actions]

PR summary 0692ef80fb

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.GroupTheory.IndexNSmul (new file)	1414

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Declarations diff

+ distribSMulToLinearMap_injective_of_isTorsionFree
+ finrank_eq_of_finiteIndex
+ finrank_eq_of_isFiniteRelIndex
+ index_range_nsmul
+ nsmulAddMonoidHom_injective_of_isTorsionFree
+ relIndex_map_nsmul

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat(Algebra/Group): some API lemmas for powMonoidHom #36458
  By Dependent Issues (🤖). Happy coding!

[artie2000]

could you provide a more descriptive name for the PR?

[MichaelStollBayreuth]

Is the PR description not good enough?

[artie2000]

it's so people (like me) skimming the review queue can quickly decide whether we will understand the maths in your PR and decide to review it (or not)

[dagurtomas]

Thanks!

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by dagurtomas.

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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• ci (staging) / Post-Build Step
• ci (staging) / Lint style
• ci (staging) / Post-CI job