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ltimes

Denotes a left semi-direct product operation, commonly used in abstract algebra and group theory.

Overview

Represents a specific type of product operation between mathematical structures, particularly important in advanced algebra and theoretical mathematics.

  • Frequently used when describing group actions and constructing new groups from existing ones
  • Essential in representing semi-direct products where one group acts on another from the left
  • Common in research papers and advanced mathematics textbooks discussing group theory
  • Often appears alongside its companion symbol \rtimes when discussing different types of group products

Examples

Defining a left semidirect product of groups G and H.

G⋉HG \ltimes H 
G \ltimes H

Expressing a left action in group theory notation.

Z2⋉Rn\mathbb{Z}_2 \ltimes \mathbb{R}^n 
\mathbb{Z}_2 \ltimes \mathbb{R}^n

Showing the structure of a wreath product construction.

A⋉(B×B)A \ltimes (B \times B) 
A \ltimes (B \times B)