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Search: MSC category 08 ( General algebraic systems )

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1. CMB 2006 (vol 49 pp. 347)

Ecker, Jürgen
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)

Grätzer, G.; Lakser, H.; Schmidt, E. T.
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)

Lipparini, Paolo
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

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