# Strongly real element

From Groupprops

*This article defines a property of elements in groups*

## Contents

## Definition

An element in a group is said to be **strongly real** if it satisfies the following equivalent conditions:

- It is either the identity element or an involution or can be expressed as a product of two distinct involutions (here an involution means a non-identity element whose square is the identity element).
- It is either the identity element or there is an involution that conjugates it to its inverse.

## Relation with other properties

### Stronger properties

### Weaker properties

### Related group properties

- Strongly ambivalent group is a group in which all the elements are strongly real elements.