TeXipedia

rtimes

Represents a binary operation symbol showing a right-tilted multiplication cross, commonly used in abstract algebra and group theory.

Overview

Denotes specialized multiplication or product operations, particularly in mathematical contexts where a distinct cross symbol is needed to differentiate from standard multiplication.

  • Frequently used in abstract algebra to represent semidirect products of groups
  • Appears in mathematical physics and advanced algebra notation
  • Often employed alongside other related binary operators to show different types of products or operations
  • Useful in contexts where standard multiplication symbols might cause ambiguity

Examples

Showing a non-normal subgroup relationship in group theory.

HG denotes the semidirect productH \rtimes G \text{ denotes the semidirect product}
H \rtimes G \text{ denotes the semidirect product}

Indicating a twisted product or crossed product in algebra.

AαGA \rtimes_\alpha G
A \rtimes_\alpha G

Representing a wreath product of groups.

C2SnC_2 \rtimes S_n
C_2 \rtimes S_n