In the paper, we provide some examples of Blackadar and Kirchberg's MF algebras by considering minimal and maximal tensor products of MF algebras and crossed products of MF algebras by finite groups or an integer group. We also present some examples of C*-algebras, which BDF extension semigroups are not groups. These examples include, for example, [Formula: see text], and [Formula: see text] with 2 ≤ |H1| < ∞ and 3 ≤ |H2| < ∞ where |H1| and |H2| are the orders of the groups H1 and H2 respectively, and several others similarly.
