It is known that, if G is a triply transitive permutation group on a finite set X with a regular normal subgroup N, then |N| = 2 (d ̂ 2) or |N| = 3. (See [12; Theorem 11.3].) If N is a regular normal subgroup of a permutation group G on X, xeX, and Gx is the stabiliser of x, then Gx £ G/JV (as abstract group), and so G has a representation on a set Y such that, for xeX, the representations of Gx...

For a finite group G, let k(G) denote the number of conjugacy classes of G. If G is a finite permutation group of degree n > 2, then k(G) ≤ 3(n−1)/2. This is an extension of a theorem of Kovács and Robinson and in turn of Riese and Schmid. If N is a normal subgroup of a completely reducible subgroup of GL(n, q), then k(N) ≤ q. Similarly, if N is a normal subgroup of a primitive subgroup of Sn, ...

introduction: the purpose of this study is to evaluate the effects of topical application of honey on the burn of full-thickness skin in rats. materials and methods: 40 adult female rats were divided into two groups and each group was subdivided into control and two experimental subgroups. the experiments were carried out under nitrofurazone anaesthesia. a third degree burn was carried out in t...

Let G be a group. The orbits of the natural action \({{\,\mathrm{Aut}\,}}(G)\) on are called automorphism G, and number is denoted by \(\omega (G)\). virtually nilpotent group such that (G)< \infty \). We prove \(G = K \rtimes H\) where H torsion subgroup torsion-free radicable characteristic G. Moreover, we \(G^{'}= D \times {{\,\mathrm{Tor}\,}}(G^{'})\) subgroup. In particular, if maximum nor...

Introduction LET dim-X be the covering dimension of a space X and let ind X and Ind X be the dimensions defined inductively in terms of the boundaries of neighbourhoods of points and closed sets respectively. The local dimension loo dim X is the least number n such that every point has a closed neighbourhood U with dim U ^ n. The local inductive dimension locIndX is defined analogously, while i...

1 Riemann Poisson manifolds were introduced by the author in [1] and studied in more details in [2]. Kähler-Riemann foliations form an interesting subset of the Riemannian foliations with remarkable properties ( see [3]). In this paper we will show that to give a regular Riemann Poisson structure on a manifold M is equivalent to to give a Kähler-Riemann foliation on M such that the leafwise sym...

The relationship between human exposure to environmental toxicants and health effects is of utmost interest to public health scientists. To define this relationship, these scientists need accurate and precise methods for assessing human exposure and effects. One of the most accurate and precise means of assessing exposure is to measure the level of the toxicant or its primary metabolite in a bi...

Abstract We determine all finite sets of equiangular lines spanning finite-dimensional complex unitary spaces for which the action on set-stabiliser in group is 2-transitive with a regular normal subgroup.

We consider a theory of gravity in which a symmetric two-index tensor in Minkowski spacetime acquires a vacuum expectation value (vev) via a potential, thereby breaking Lorentz invariance spontaneously. When the vev breaks all the generators of the Lorentz group, six Goldstone modes emerge, two linear combinations of which have properties that are identical to those of the graviton in general r...

‎let $g$ be a finite group and let $n$ be a normal subgroup of $g$‎. ‎suppose that ${rm{irr}} (g | n)$ is the set of the irreducible characters of $g$ that contain $n$ in their kernels‎. ‎in this paper‎, ‎we classify solvable groups $g$ in which the set $mathcal{c} (g) = {{rm{irr}} (g | n) | 1 ne n trianglelefteq g }$ has at most three elements‎. ‎we also compute the set $mathcal{c}(g)$ for suc...