If we compare these results to the ones in Example 4.1 in , where the authors considered the Klein bottle to be a solvmanifold, we also find that for n = [2.sup.m],
Note that they actually proved a more general version of this theorem, as they showed that the theorem above also holds for solvmanifolds.
Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds I.
By the literal meaning, an infra-solvmanifold is a smooth manifold finitely covered by a solvmanifold (which is the quotient of a connected solvable Lie group by a closed subgroup).
Tuschmann, Collapsing, solvmanifolds and infrahomogeneous spaces, Differential Geom.
The paper  exhibited for each solvmanifold (and a fortiori for nilmanifolds) a model solvmanifold that had exactly the same Nielsen theory (N([f.sup.m]), N[P.sub.m](f) and N[[PHI].sub.m](f)) as any map f on the original solvmanifold.
Ed was present at the conception of the paper which flowed out of a joint project, started way back in 1994/5, to study the Nielsen periodic point numbers on solvmanifolds. What was left over from the project was the study of these numbers on the special class of periodic maps on these spaces.
 Heath Philip R., Keppelmann E., Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds I, Top.
Affine translation surfaces in Huili LIU and Yanhua YU Euclidean 3-space On the equivalence of several Shintaro KUROKI and Li YU definitions of compact infra- solvmanifolds
Duc Tai PHO Alexander polynomials of certain Above three, communicated by dual of smooth quartics Kenji FUKAYA, M.J.A.
Padron: New examples of compact cosymplectic solvmanifolds
McCord, Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds
II, Topology Appl., 75 (1997), 81-?92.
 Edward Keppelmann, Periodics points on nilmanifolds and solvmanifolds
, Pacific Journal of Mathematics, vol.164 (1) (1994), 105-128.