It is known that if $p>37$ a prime number and $E/\mathbb{Q}$ an elliptic curve without complex multiplication, then the image of mod $p$ Galois representation $$ \bar{\rho}_{E,p}:\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\rightarrow \operatorname{GL}(E[p]) $E$ either whole $\operatorname{GL}(E[p])$, or \emph{contained} in normaliser non-split Cartan subgroup $\operatorname{GL}(E[p])$....

We compare the sequences for the mitochondrial cytochrome oxidase II gene of 13 species of the Drosophila obscura group. The survey includes six members of the D. affinis subgroup, four of the D. pseudoobscura subgroup, and three of the D. obscura subgroup. In all species, the gene is 688 nucleotides in length, encoding a protein of 229 amino acids plus the first position T of the stop codon. T...

We study finite groups G having a normal subgroup H and \(D \subset \setminus H, D \cap D^{-1}=\emptyset ,\) such that the multiset \(\{ xy^{-1}:x,y \in D\}\) has every non-identity element occur same number of times (such is called DRAD difference set). show there are no order \(4p^2\), where p an odd prime.

Abstract Shalom and Tao showed that a polynomial upper bound on the size of single, large enough ball in Cayley graph implies underlying group has nilpotent subgroup with index degree growth both bounded effectively. The third fourth authors proved optimal this subgroup, at expense making some other parts result ineffective. In present paper, we prove without any losses elsewhere. As consequenc...

In this paper we recognize the topological type of the group D(R) of C diffeomorphisms of the real line, endowed with the Whitney C-topology (cf. [6]). Besides the whole group D(R) we shall also be interested in its subgroup D c (R) ⊂ D (R) consisting of diffeomorphisms f : R → R with compact support supp(f) = clR{x ∈ R : f(x) 6= x}. For n = 0 the topological group D(R) turns into the homeomorp...

The allele amplification and diversity of 18 microsatellite loci described for Drosophila mediopunctata (tripunctata group) was studied in two species of the Drosophila guarani group, D. ornatifrons (guarani subgroup) and D. maculifrons (guaramunu subgroup), collected in fragments of Araucaria Forest from southern Brazil. The selected loci were already tested in lineages of both species from D....

We construct a large family of positive definite kernels $K: \mathbb D^n\times D^n \to \mathrm M (r, C)$, holomorphic in the first variable and anti-holomorphic second, that are quasi-invariant with respect to subgroup Möb$\,\ti

Response to wing-web challenge (WWC) of Rous sarcoma virus (RSV) subgroups was studied in 4-8 weeks old chicks of a light breed, a heavy breed and a cross between an indigenous black plumage Bantam fowl and Australorp breed. Wing-web tumor (WWT) began to develop within one week in response to virus subgroups A (BS-RSV) and C [RSV (RAV-49)] challenge. In chicks challenged with subgroup D [RSV (R...