we analyze some properties of the distribution $q_{g,k}$ of the first component in a $k$-tuple chosen uniformly‎ ‎in the set of all the $k$-tuples generating a finite group $g$ (the limiting distribution of the product replacement algorithm)‎. ‎in particular‎, ‎we concentrate our attention on‎ ‎the study of the variation distance $beta_k(g)$ between $q_{g,k}$ and the uniform distribution‎. ‎we ...

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qual­ itative property called product synergy. The current definition of product synergy is insuf­ ficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new defi...

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool the study of regular Cayley maps and, more generally, finite groups with complementary factorisation $G=BY$, where $Y$ is cyclic and core-free in $G$. In this paper, we classify all examples $B$ monolithic (meaning that it has unique minimal normal subgroup, subgroup not abelian) As consequence, obtain classif...

Abstract. The holomorph of a discrete group G is the universal semi-direct product of G. We construct a resolution for Hol(Zpr ) for every prime p, where Zm denotes a cyclic group of order m, and use it to compute the integer homology and mod p cohomology of Hol(Zpr ) (this computation is long and is omitted here, but will appear in [V]). Also, we study maps of holomorphs of groups and maps of ...

For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P : the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of their centers. Unlike for direct product decompositions, AutP is not always transitive on the set of fully refined central decompositions, and the number of orb...

We compute the group homology, the topological K-theory of the reduced C∗-algebra and the algebraic Kand L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1 → K → G → Q → 1 of a torsionfree group K by a group Q whi...

Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...