A rational group of hermitian type is a Q-simple algebraic group G such that the symmetric space D of maximal compact subgroups of the real Lie group G(R) is a hermitian symmetric space of the non-compact type. There are two major classes of subgroups of G of importance to the geometry of D and to arithmetic quotients XΓ = Γ\D of D: parabolic subgroups and reductive subgroups. The former are co...

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

Let $$D$$ be a division ring and $$K$$ subfield of which is not necessarily contained in the center $$F$$ . We study structure under condition left algebraicity certain subsets over Among others, it proved that if $$D^*$$ contains noncentral normal subgroup algebraic bounded degree $$d$$ , then $$[D:F]\le d^2$$ In case $$K=F$$ obtained results show either all additive commutators or multiplicat...

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...

We study finite groups that occur as combinatorial automorphism or geometric symmetry of convex polytopes. When $\Gamma$ is a subgroup the group $d$-polytope, $d\geq 3$, then there exists $d$-polytope related to original polytope with exactly $\Gamma$. both and These symmetry-breaking results are applied show for every abelian even order involution $\sigma$ $\Gamma$, centrally symmetric such co...

This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup the general skew linear group $\GL_n(D)$ over a division ring $D$. It turns out that in case where $D$ is non-commutative, if such exist, then either it abelian or $[D:F]<\infty$. Also, $F$ infinite field $n\geq 5$, every normal $\GL_n(F)$ abelian.

Retrosequences, genes, and pseudogenes originated by retrotranscription are frequent components of vertebrate genomes, but they have only occasionally been described in invertebrates. In Drosophila, very few retrosequences have been reported, among them those of alcohol dehydrogenase (Adh) and phosphoglyceromutase (Pglym). Although 52 Adh gene sequences are available for comparison, Adh retrose...

Division algebras D generated by some finitely generated nilpotent subgroup G of the multiplicative group D* of D are studied and the question to what extent G is determined by D is considered. Trivial examples show that D does not determine G up to isomorphism. However, it is proved that if F denotes the center of D, then the F-subalgebra of D generated by G is in fact determined up to isomorp...

The distribution of the transposable element mariner was examined in the genus Drosophila. Among the eight species comprising the melanogaster species subgroup, the element is present in D. mauritiana, D. simulans, D. sechellia, D. yakuba and D. teissieri, but it is absent in D. melanogaster, D. erecta and D. orena. Multiple copies of mariner were sequenced from each species in which the elemen...