In this paper we study affine completeness of generalised dihedral groups. We give a formula for the number of unary compatible functions on these groups, and we characterise for every $k \in~\N$ the $k$-affine complete generalised dihedral groups. We find that the direct product of a $1$-affine complete group with itself need not be $1$-affine complete. Finally, we give an example of a nonabelian solvable affine complete group. For nilpotent groups we find a strong necessary condition for $2$-affine completeness.

We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) {\it semimodular} lattice.

We provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to the TC-commutator iff it has a (weak) difference term (is neutral) with respect to the linear commutator. We show that a variety \v\ is congruence meet semi-distributive i{f}f \v\ is neutral, i{f}f $M_3$ is not a sublattice of \con a, for ${\bf A} \in \v$, i{f}f there is a positive integer $n$ such that $\v \smc \a(\b\o\g)\leq\alpha \beta_n$.