S h → G R Ad → GL(g) Concretely, C× acts on gC via the characters z/z, 1, z/z. (2) ad(h(±i)) is a Cartan involution of G(R). (3) There is no Q-simple factor Gi of G such that S h → G R → G i,R is trivial. 1.2.2. Remark. Brian gave a slightly different defintion of a connected Shimura datum, using the continuous map u : S → G(R) obtained by restricting h(R) to the unit circle S ⊂ C× = S(R). This...

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in this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. the illustrated results are joint works with john cannon, dan levy, attila mar'oti and iulian i. simion.

A subgroup of V containing a principal congruence subgroup T(«) is said to be a congruence subgroup, and is of level « if « is the least such integer. In a recent article [2] the writer determined all normal subgroups of T of genus 1 (see [l] for the definition of the genus of a subgroup of r). An interesting question that arises is to decide which of these are also congruence subgroups. In thi...

Let $X$ be a smooth projective quadric defined over field of characteristic 2. We prove that in the Chow group codimension 2 or 3 torsion subgroup has at most two elements. In 2, we determine precisely when this is nontrivial. 3, show there no if $\dim X\ge 11$. This extends analogous results different from obtained by Karpenko nineteen-nineties.

Associated to a convex integral polygon $N$ is cluster integrable system $\mathcal X\_N$ constructed from the dimer model. We compute group $G\_N$ of symmetries X\_N$, called (2-2) modular group, showing that it certain abelian conjectured by Fock and Marshakov. Combinatorially, non-torsion elements are ways shuffling underlying bipartite graph, generalizing domino-shuffling. Algebro-geometrica...

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎

We studied the molecular genetic background of the B subgroup in the Chinese Han population and identified a novel allele at the ABO locus. Ten control samples from randomly selected blood donors of normal B phenotype and 6 samples from individuals diagnosed as B subgroup by serological tests were genotyped by PCR-SSP and direct DNA sequencing at exons 6 and 7 of the ABO gene. Exons 6 and 7 and...

We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety G defined over a finite field with a closed subvariety X ⊂ G.