The essential ideal is a Cohen-Macaulay module

Let G be a finite p-group which does not contain a rank two elementary abelian p-group as a direct factor. Then the ideal of essential classes in the mod-p cohomology ring of G is a Cohen-Macaulay module whose Krull dimension is the p-rank of the centre of G. This basically answers in the affirmative a question posed by J. F. Carlson.Comment: 6 page

Lightweight ceramic insulation and method

A process is disclosed for manufacturing a low density ceramic powder which can be formed to make a lightweight material for insulation or other construction. The ceramic product made from the process has a final density of less than 25 to about 1 percent of the theoretical weight of the ceramic powder. The ceramic product is lightweight and can be made to withstand high temperatures greater than 1400 C

Appendix B: Some morphometric parameters of named lakes with areas [greater than or equal to] 1.0 km2, and some smaller lakes, in New Zealand

Gaps indicate uncertainty or that accurate data are unavailable. Note that lakes with fluctuating levels e.g., those used for hydro-electric purposes, or near coasts have varying parameters. Table based mainly on Irwin (1975) with some data from Cunningham et al. (1953), Irwin (1972), Jolly & Brown (1975), Irwin & Pickrill (1983), Howard-Williams & Vincent 1984, Boswell et al. (1985), Livingstone et al. (1986), N.Z.O.I. Lake Chart series, N.Z. Topographical Map Series NZMS1 (1:63 360) and NZMS26O (1:50 000), and other sources

Lakes

Lakes have always held an aesthetic fascination for people; they figure prominently in both art and literature and have even been endowed with spiritual qualities. For example, the nineteenth century American writer Henry D. Thoreau (1854) considered a lake to be 'the landscape's most beautiful and expressive feature. It is the earth's eye; looking into which the beholder measures the depth of his own nature'. More prosaically, lakes are also of considerable geomorphological interest as dynamic landfonns originating in varied and often complex ways

The computation of the cohomology rings of all groups of order 128

We describe the computation of the mod-2 cohomology rings of all 2328 groups of order 128. One consequence is that all groups of order less than 256 satisfy the strong form of Benson's Regularity Conjecture.Comment: 15 pages; revised versio