Strongly real element

This article defines a property of elements in groups

Definition

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

1. 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).
2. It is either the identity element or there is an involution that conjugates it to its inverse.

Relation with other properties

Stronger properties

• Involution

Weaker properties

• Real element

Related group properties

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