# Approximate normalizer

This is a variation of normalizer|Find other variations of normalizer |

## Contents

This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

## Definition

### Definition with symbols

Let $G$ be a group and $g \in G$ be an element. Then, the approximate normalizer of $g$, denoted as $N_G^*(g)$ is defined as the set of all elements $t \in G$ for which there exist nonzero integers $m,n$ such that $t^{-1}g^mt = g^n$.

The approximate normalizer of any element is a subgroup of the whole group. It equals the whole group if the element has finite order (viz, is a torsion element). Thus, the notion makes sense to study only for elements of infinite order.

## References

• On a certain infinite permutation group by Graham Higman, J. Algebra 131 (1990), 359-369