---
tag: 52BNYXGVCV
kind: concept
name: Real element
aliases: [extended-centralizer, strongly-real-element]
sources:
  - wikipedia: en:50475634@r1121784856
    locator: Real element
    note: adopted
    mention: wikipedia://en/50475634
    sections: [Summary]
same_as:
  wikidata: Q25105219
  wikipedia: Real element
inventory: [C3CWBVKB38]
---

## Summary

In group theory, a discipline within modern algebra, an element $x$ of a group $G$ is called a **real element** of $G$ if it belongs to the same [[conjugacy class|0DEBXAJ5SA]] as its [[inverse|0BRHKKP333]] $x^{-1}$, that is, if there is a $g$ in $G$ with $x^g = x^{-1}$, where $x^g$ is defined as $g^{-1} \cdot x \cdot g$. An element $x$ of a group $G$ is called **strongly real** if there is an involution $t$ with $x^t = x^{-1}$.