TeXipedia

lhd

Represents a left-pointing triangular binary relation operator commonly used in abstract algebra and set theory.

Overview

Serves as a mathematical symbol denoting specific relationships between elements or structures, particularly in group theory and order theory.

  • Often used to indicate subgroup relations or partial ordering.
  • Frequently appears alongside its companion symbol \rhd in mathematical proofs and formal definitions.
  • Common in academic papers and textbooks discussing algebraic structures.
  • Particularly useful when describing normal subgroups and semidirect products in advanced algebra.

Examples

Showing a normal subgroup relation in group theory.

H⊲GH \lhd G 
H \lhd G

Expressing a proper normal subgroup chain.

H1⊲H2⊲H3⊲GH_1 \lhd H_2 \lhd H_3 \lhd G 
H_1 \lhd H_2 \lhd H_3 \lhd G

Demonstrating normal subgroup with specific groups.

S3⊲S6S_3 \lhd S_6 
S_3 \lhd S_6