Title: Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian group,
Abstract: Let $X$ be a locally compact Abelian group, $Y$ be its character group.
Following A. Kagan and G. Székely we introduce a notion of $Q$-independence
for random variables with values in $X$. We prove group analogues of the
Cramér, Kac-Bernstein, Skitovich-Darmois and Heyde theorems for
$Q$-independent random variables with values in $X$. The proofs of these
theorems are reduced to solving some functional equations on the group $Y$.