In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

We introduce the problem of robust subgroup discovery, i.e., finding a set interpretable descriptions subsets that 1) stand out with respect to one or more target attributes, 2) are statistically robust, and 3) non-redundant. Many attempts have been made mine either locally subgroups tackle pattern explosion, but we first address both challenges at same time from global modelling perspective. F...

we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.

Background and objective: Many clinical trials have revealed that HMG-CoA reductase inhibitors (statins) anti-inflammatory effects through their pleiotropic activities there by decreasing the risk of cardiovascular disease (CVD). This study intended to evaluate effect rosuvastatin on level inflammatory markers (hsCRP, IL-6, sCD40L, Lp-PLA2, cystatin C) in normotensive hypertensive rats. Methods...

We are concerned with conditions under which a locally compact group G has a maximal compact normal subgroup K and whether or not G/K is a Lie group. If G has small compact normal subgroups K such that G/K is a Lie group, then G is pro-Lie. If in G there is a collection of closed normal subgroups {Ha} such that f~| Ha = e and G/Ha is a Lie group for each a, then G is a residual Lie group. We de...

The discovery of (interesting) subgroups has a high practical relevance in all domains of science or business. For example, consider statements such as: ”the unemployment rate is above average for young men with a low educational level”, ”smokers with a positive family history are at a significantly higher risk for coronary heart disease”, or ”single males living in rural areas do rarely take o...

Let G be a connected real Lie group. The universal representation kernel, Ko, oí G is defined as the intersection of all kernels of continuous finite dimensional representations of G. Evidently, Ko is a closed normal subgroup of G, and it is known from a theorem due to Goto (cf. [l, Theorem 7.1]) that G/Ko has a faithful continuous finite dimensional representation. Thus Kg is the smallest norm...