Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...

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 $sp_6(2)$.

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...

Thiopurine S-methyltransferase (TPMT) is an enzyme that converts thiopurine drugs into inactive metabolites. Over 20 variant TPMT-encoding alleles, which cause reduced enzymatic activity, have been discovered so far. Our aim was to investigate the frequencies of variant alleles, i.e. genotypes in inflammatory bowel disease (IBD) patients and healthy individuals and to compare these frequencies ...

Avian leukosis viruses (ALVs) are common in many poultry flocks and can be detected using an enzyme-linked immunosorbent assay or any other test designed to identify p27, the group-specific antigen located in gag. However, endogenous retroviruses expressing p27 are often present and can be confused with exogenous ALVs. A more specific and informative assay involves targeting the variable envelo...