Conjugacy classes of primitive words in the free group of rank two can indexed by the rationals. A representative for each conjugacy class is given by a recursive enumeration scheme and the representative, usually called a Farey word, is denoted by Wp/q where p and q are relatively prime integers. Primitive pairs, that is, pairs of words that generate the free group, correspond to pairs of word...

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding 'imprimitive wreath decomposition concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The r...

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

Production results were compared for two groups of turkeys reared in semi-intensive system. The material included 40 primitive turkeys of the light type and 40 heavy hybrids of the Big-6 line (commercial flock). Females was raised to 14 and males to 22 weeks of life. During the rearing, body weight (g) was controlled individually and feed intake (g) was monitored in groups, in weekly intervals....

Let G be a transitive permutation group acting on a finite set E and let P be the stabilizer in G of a point in E. We say that G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1H the permutation character (or permutation module) over C of G on the cosets G/H. Let H and K be subgroups of G. We say 1H 6 1 G K if 1 G K − 1 G...

Many famous graphs are edge-primitive, for example, the Heawood graph, the Tutte–Coxeter graph and the Higman–Sims graph. In this paper we systematically analyse edge-primitive and edge-quasiprimitive graphs via the O’Nan–Scott Theorem to determine the possible edge and vertex actions of such graphs. Many interesting examples are given and we also determine all G-edge-primitive graphs for G an ...

We characterise the primitive 2-closed groups G of rank at most four that are not automorphism group a graph or digraph and show if degree is least 2402 then there just two infinite families G⩽AΓL1(pd), 1-dimensional affine semilinear group. These first known examples non-regular digraph.

Many famous graphs are edge-primitive, for example, the Heawood graph, the Tutte–Coxeter graph and the Higman–Sims graph. In this paper we systematically analyse edge-primitive and edge-quasiprimitive graphs via the O’Nan–Scott Theorem to determine the possible edge and vertex actions of such graphs. Many interesting examples are given and we also determine all G-edge-primitive graphs for G an ...

3.18.3 CHARACTERISTICS OF ARC MAGMAS 7 3.18.3.1 Comparison with MORBs 7 3.18.3.1.1 Major elements 7 3.18.3.1.2 We are cautious about fractionation correction of major elements 9 3.18.3.1.3 Distinctive, primitive andesites 11 3.18.3.1.4 Major elements in calc-alkaline batholiths 11 3.18.3.2 Major and Trace-Element Characteristics of Primitive Arc Magmas 18 3.18.3.2.1 Primitive basalts predominat...