Finite Groups 20Dxx [1] A. Adem, J. F. Carlson, D. B. Karagueuzian, and R. James Milgram, The cohomology of the Sylow 2-subgroup of the Higman-Sims group, J. Pure Appl. Algebra 164 (2001), no. 3, 275–305. MR MR1857743 (2002g:20089) [2] Faryad Ali and Jamshid Moori, Fischer-Clifford matrices of the non-split group extension 2 · U4(2), Quaest. Math. 31 (2008), no. 1, 27–36. MR MR2404644 [3] Habib...

The Arithmetic is interpreted in all the groups of Richard Thompson and Graham Higman, as well as in other groups of piecewise affine permutations of an interval which generalize the groups of Thompson and Higman. In particular, the elementary theories of all these groups are undecidable. Moreover, Thompson’s group F and some of its generalizations interpret the Arithmetic without parameters.

A distance-transitive graph G is one upon which the automorphism group acts transitively on ordered pairs of vertices at every fixed distance. Only connected graphs need to be considered. Those of diameter 2 are the rank-3 graphs, whose careful study was initiated by Donald G. Higman in his breakthrough paper [16]. A huge amount of effort has gone into the classification of all finite distancet...

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...

Abstract In the context of Higman embeddings recursive groups into finitely presented groups, we suggest an approach, termed

The talk will summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schroedinger operators with random potential, quantum graph operators for trees with randomized edge lengths, and Schroedinger operators with radial quasi-periodic potentials. The results were derived jointly with R. Sims and S....

A $P_4$-free graph is called a cograph. In this paper we partially characterize finite groups whose power As will see, problem generalization of the determination in which every element has prime order, first raised by Graham Higman 1957 and fully solved very recently. First determine all $G$ $H$ for $G\times H$ We show that cograph can be characterised condition only involving elements orders ...