Let V (ZG) be the normalized unit group of the integral group ring ZG of a finite group G. One of most interesting conjectures in the theory of integral group ring is the conjecture (ZC) of H. Zassenhaus [25], saying that every torsion unit u ∈ V (ZG) is conjugate to an element in G within the rational group algebra QG. For finite simple groups, the main tool of the investigation of the Zassenh...

Symmetries of a Place/Transition-net can be exploited during the reachability analysis by considering only one representative marking in each orbit induced by the symmetries. In this report, three new algorithms for transforming a marking into a symmetric canonical representative marking are described. All the algorithms depend on the precalculation of a SchreierSims representation for the symm...

We show that for the family of Church-Rosser languages the Higman-Haines sets, which are the sets of all scattered subwords of a given language and the sets of all words that contain some word of a given language as a scattered subword, cannot be effectively constructed, although these both sets are regular for any language. This nicely contrasts the result on the effectiveness of the Higman-Ha...

If a graph attains the bound (1.1) it is called a Moore graph if g is odd and a generalised polygon if g is even. A lot of work has been done on the classification of these graphs. Moore graphs have been studied by Hoffman and Singleton [8], Bannai and Ito [1], and Damerell [5]. Generalised polygons have been studied by Feit and Higman [7], Benson [3], and Singleton [9]. Biggs ([4]; Chapter 23)...

Well known Sims conjecture proved by P. J. Cameron, C. E. Praeger, J. Saxl and G. M. Seitz (1983) can be formulated as follows. Let be an undirected connected nite graph and G be a subgroup of Aut acting primitively on the vertex set V ( ) of . For x 2 V ( ) and positive integer i, denote by G x the point-wise stabilizer in G of the closed ball of the radius i with the center x of the graph . T...

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...

A not so well-known result in formal language theory is that the Higman-Haines sets for any language are regular [11, Theorem 4.4]. It is easily seen that these sets cannot be effectively computed in general. The Higman-Haines sets are the languages of all scattered subwords of a given language as well as the sets of all words that contain some word of a given language as a scattered subword. R...

We use category-theoretic techniques to provide two proofs showing that for a higher-rank graph Λ \Lambda </inl...