# Witt's identity

From Groupprops

This fact is related to: commutator calculus

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## Contents

## Statement

### In terms of right-action convention

Let be elements of an arbitrary group . Then:

where and , and is the identity element of the group.

## Related results

## Proof

### In terms of right-action convention

**Given**: A group , elements . is the identity element.

**To prove**: where and .

**Proof**: We start out with the first term on the left side:

Similarly, we have:

and:

Multiplying these, all terms cancel and we obtain the identity element, as desired.