\rtimesThe \rtimes symbol is used to denote a semidirect product in group theory. It is an operation that combines two groups into a new group, where one group acts on the other in a specific way. The semidirect product is a generalization of the direct product of groups, allowing for more complex interactions between the groups.
Semidirect product of groups G and H
G \rtimes HSemidirect product with a homomorphism \phi defining the action of H on N
N \rtimes_\phi HSemidirect product of the integers with the cyclic group of order 2
\mathbb{Z} \rtimes \mathbb{Z}_2