Strongly real element

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This article defines a property of elements in groups


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

Weaker properties

Related group properties