# Group theory – Product of the inner garland.

The standard definition of internal semidirect product says that $$G$$ is a semi-direct product of $$K$$ Y $$H$$ Yes $$G = KH$$, for some subgroup $$K$$ Y $$H$$ of $$G$$ such that $$K$$ It is normal and $$K cap H = {H }$$.

Generally garland product of groups. $$K wr H$$ It is defined as and external semidirect product with $$K ^ n rtimes_ Phi H$$, where $$Phi$$ it is a homomorphism $$H a Aut (K ^ n)$$.

Is it possible to define an inner crown product without talking about homomorphism, that is, simply decomposing a group into some subgroups that satisfy some conditions?