# Rational and nilpotent implies 2-group

From Groupprops

## Contents

## Statement

Suppose is a group that is both a Rational group (?) and a Nilpotent group (?). Then, must be a 2-group, i.e., it is a group in which every element has finite order and the order is a power of 2.

## Related facts

## Facts used

## Proof

The proof follows directly from Facts (1) and (2).