Real element
In group theory, a discipline within modern algebra, an element x {\displaystyle x} of a group G {\displaystyle G} is called a real element of G {\displaystyle G} if it belongs to the same conjugacy class as its inverse x − 1 {\displaystyle x^{-1}} , that is, if there is a g {\displaystyle g} in G {\displaystyle G} with x g = x − 1 {\displaystyle x^{g}=x^{-1}} , where x g {\displaystyle x^{g}} is defined as g − 1 ⋅ x ⋅ g {\displaystyle g^{-1}\cdot x\cdot g} . An element x {\displaystyle x} of a group G {\displaystyle G} is called strongly real if there is an involution t {\displaystyle t} with x t = x − 1 {\displaystyle x^{t}=x^{-1}} .