Chevalley's theorem for affine Nash groups

TL;DR

This paper extends Chevalley's theorem to affine Nash groups and demonstrates that the semi-direct product of two almost linear Nash groups retains the almost linear property, advancing the understanding of Nash group structures.

Contribution

It formulates and proves Chevalley's theorem within the context of affine Nash groups, establishing new structural results for Nash groups.

Findings

Chevalley's theorem is valid for affine Nash groups.

The semi-direct product of two almost linear Nash groups is almost linear.

Provides foundational results for the structure theory of Nash groups.

Abstract

We formulate and prove Chevalley's theorem in the setting of affine Nash groups. As a consequence, we show that the semi-direct product of two almost linear Nash groups is still an almost linear Nash group.