It is not difficult to see that a group ring $K[G]$ ($K$ a domain) has non-trivial zero-divisors whenever there exists a non-trivial torsion element $g\in G$. [In fact, in this case, $1-g$ is such a non-trivial zero-divisor]
My question is the following: is it possible that a crossed product $K*G$ is a domain even if $G$ has non-trivial torsion (e.g., what happens when $G$ is finite)?
My guess is that $K*G$ may very well be a domain. In fact, if $G'$ is a group such that $K*G'$ is a domain and $G=G'/H$ is quotient of $G'$ (I'm thinking for example to the case $G'=\mathbb Z$ and $G=\mathbb Z(p)$), then $D=K*H$ is a domain and so $K*G'=D*(G'/H)=D*G$ cannot have non-trivial zero divisors. It seems that this example answers my question but in a very indirect way... do you have any straightforward reason for which this phenomenon may happen? Thank you in advance.