We consider the wreath product of two symmetric groups as a group blocks permutations and we study its conjugacy classes. give polynomiality property for structure coefficients center algebras. This allows us to recover an old result Farahat Higman about algebra generalize our recent hyperoctahedral algebra.

We prove that the number of groups of order p whose Frattini subgroup is central is for fixed n a PORC (‘polynomial on residue classes’) function of p. This extends a result of G. Higman.

In this paper, we will prove the inevitable non-uniformity of two constructions from combinatorial group theory related to the word problem for finitely generated groups and the Higman-Neumann-Neumann Embedding Theorem.

We show that Brin’s generalisations 2V and 3V of the Thompson-Higman group V are of type FP∞. Our methods also give a new proof that both groups are finitely presented.

THE concept of HNN-extensions of groups was introduced by Higman, Neumann and Neumann in 1949. HNN-extensions and amalgamated free products have played a crucial role in combinatorial group theory, especially for algorithmic problems. In inverse semigroup theory there are many ways of constructing HNNextension in order to ensure the embeddability of the original inverse semigroup in the new one...

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

Damage introduced by dynamic secondary ion mass spectrometry ~SIMS! depth profiling is studied. A silicon sample with a boron marker layer was depth profiled by dynamic SIMS. After subsequent annealing at 750 °C for 30 min, the SIMS sample was reanalyzed by plan-view transmission electron microscope ~PTEM! and SIMS. PTEM images showed the presence of interstitial defects near the original SIMS ...