# Multiplicative properties of the multiplicative group

## TL;DR

This paper explores properties of the multiplicative group that are equivalent to the norm residue isomorphism theorem, providing insights into the structure and implications of the Bloch-Kato conjecture.

## Contribution

It establishes new equivalences related to the Bloch-Kato conjecture through properties of the multiplicative group.

## Key findings

- Identifies properties equivalent to the Bloch-Kato conjecture
- Provides new characterizations of the norm residue isomorphism theorem
- Enhances understanding of the multiplicative group's role in algebraic K-theory

## Abstract

We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).