TeXipedia

wr

Represents a wreath product operation, commonly used in abstract algebra and group theory.

Overview

Denotes a specific type of group construction that combines two groups into a larger, more complex structure. Particularly important in advanced mathematics where:

  • Used to construct semidirect products of groups
  • Appears frequently in representation theory
  • Essential in studying symmetry groups and permutation groups
  • Common in theoretical computer science when analyzing automata and formal languages

Examples

Wreath product in group theory notation.

G≀HG \wr H 
G \wr H

Expressing the wreath product of symmetric groups.

Sn≀SmS_n \wr S_m 
S_n \wr S_m

Complex wreath product in algebraic structure.

Z2≀Z3\mathbb{Z}_2 \wr \mathbb{Z}_3 
\mathbb{Z}_2 \wr \mathbb{Z}_3