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1. CMB 2006 (vol 49 pp. 347)
Affine Completeness of Generalised Dihedral Groups 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.
Categories:08A40, 16Y30, 20F05 |
2. CMB 1998 (vol 41 pp. 290)
Congruence lattices of finite semimodular lattices We prove that every finite distributive lattice can be represented
as the congruence lattice of a finite (planar) {\it semimodular}
lattice.
Categories:06B10, 08A05 |
3. CMB 1998 (vol 41 pp. 318)
A characterization of varieties with a difference term, II: neutral $=$ meet semi-distributive 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 $\v \smc
\a(\b\o\g)\leq\alpha \beta_n$.
Categories:08B05, 08B99 |