Fellowship of the Australian Academy of Science and Fellowship of the Australian College of Education are formal recognition of Hanna Neumann's impact on a country she had first set foot in only in August 1963. But then`Hanna Neumann was a remarkable person. Throughout her life she had won the love and respect of many people. The extent of this can not really be measured, however some indications can be given. A memorial meeting held in Canberra overflowed a large lecture theatre even though it was virtually vacation time. A collection of papers dedicated to her memory and a fund to provide some form of memorial to her have both drawn quite overwhelming support from many parts of the world. One finds a tremendous list of words describing her memorable qualities: warm, enthusiastic, inspiring, energetic, firm, tactful, sympathetic, efficient, patient, shrewd, humble, peace-loving, courageous, gracious, … No words can hope to evoke more than a pale shadow of such a person; this story must be read in such a light.

The problem of diffraction of a Kelvin wave by a narrow opening in a barrier separating two semi-infinite sheets of water is formulated as an integral equation. An approximate solution is obtained on the hypothesis that the gap is small compared with the length of the incident wave. The scattered disturbance comprises both Kelvin and Poincaré waves, and asymptotic formulate for their amplitudes are obtained. The results, which are relevant to tidal diffraction by a strait, reveal that the phase shift in the diffracted Kelvin wave is much larger than the corresponding shift induced by either a narrow channel or an inland sea opening into a semi-infinite ocean.

If x and y are elements in the group G, then we denote their commutator by x o y = x-1y-1 = x-1xy; and x o G is the set of all commutators x o g with g ∈ G. A G-commutator sequence is a series of elements ci ∈ G with c1 + 1 ∈ ci O G. Slightly generalizing well known results one proves that the hypercenter of the group G is exacly the set of all elements h ∈ G with the property: every G-commutator sequence, containing h, contains 1 [Proposition 1.1].

LetP1, P2…, pN be N points in the unit s-dimensional closed square Q = [0, 1]s. For any measurable set S ⊆ Q, we define δ(S), the discrepancy of S, by , where V(S) is the s-dimensional volume of S, and n(S), is the number of indices i for which pi∈S. Let , where the supermum is taken over all s-balls B ∈ Q, and , the supermum in this case being taken over all convex sets C ∈ Q. Clearly Dc ≧ Dk. In this paper we establish Theorem , where φ1is a constant depending only on s.

This paper is concerned with version of Bernstein's inequality for Hausdroff locally compact Abelian groups. The ideas used are suggested by Exercise 12, p. 17 of Katznelson's book [4].

The first and still the best known computer application to groups exploits coset enumeration and this has been very thoroughly studied; see for instance [2] and [8]. No doubt this is because the algorithm is simple in the sense of programming. The Underlying mathematics is far from simple, touching as it does no logical difficulties akin to the word problem for groups, and this is reflected in the facts that random access to large tables is required and that there is no indication at any stage (for example when storage space is exhausted) whether the algorithm would be completed at any later stage. Efficient computation depends on choosing a subgroup of small index m in the group under examination, for group elements will be represented as permutations of degree m, and the larger m is the more tedious it will be to check properties like orders of group elements. Yet in many cases m may have to be fairly large so that the subgroup is “corefree” i.e. the representation is faithful.

A subgroup H of a group G is said to be subnormal in G if there is a finite chain of subgroups, each normal in its successor, connecting H to G. If such chains exist there is one of minimal length; the number of strict inclusions in this chain is called the subnormal index, or defect, of H in G. The rather large class of groups which have an upper bound for the subnormal indices of their subnormal subgroups has been inverstigated to same extent, mainly with a restriction to solublegroups — for instance, in [10] McDougall considered soluble p-groups in this class. Robinson, in [14], restricted his attention to wreath products of nilpotent groups but extended his investigations to the strictly larger class of groups in which the intersection of any family of subnormal subgroups is a subnormal subgroup. These groups are said to have the subnormal intersection property.