We study the subgroup structure of discrete groups which share cohomological properties which resemble non-negative curvature. Examples include all Gromov hyperbolic groups. A subgroup H ⊂ G is called s-normal, if H∩H is infinite for all g ∈ G. We provide strong restrictions on the possible s-normal subgroups of a Gromov hyperbolic group, or more generally a ’negatively curved’ group. Another r...

In the study of the relation between the mapping class group ? g of a surface g of genus g and the theory of nite-type invariants of homology 3-spheres, three subgroups of ? g play a large role. They are the Torelli group T g , the Johnson subgroup K g and a new subgroup L L g , which contains K g , deened by a choice of a Lagrangian subgroup L H 1 ((g). In this work we determine the quotient L...

An f-subgroup is a linear recurring sequence subgroup, multiplicative subgroup of field whose elements can be generated (without repetition) by recurrence relation, where the relation has characteristic polynomial f . It called non-standard if it in non-cyclic way (that is, not order ? i , + 1 2 … for zero ), and standard otherwise. We will show that finite -subgroup necessarily subset zeros us...

We report on the Modeling Across the Curriculum Project (mac.concord.org), a 5-year study funded by the IERI program (IERI # 0115699). In this project we are using qualitative model-based tools for inquiry in three science domains (Genetics, Gas Laws, & Newtonian Mechanics) to promote scientific literacy on a broad scale, namely, content knowledge, process skills, and epistemologies of science ...

Let Fn denote a free group of rank n. The group Out(Fn) contains mapping class groups of compact surfaces and maps onto GL(n,Z). It is perhaps not surprising that Out(Fn) behaves at times like a mapping class group and at times like a linear group. J. Birman, A. Lubotzky, and J. McCarthy [BLM83] showed that solvable subgroups of mapping class groups are finitely generated and virtually abelian....

Information-­‐‑ related measures are useful tools for multi-­‐‑ variable data analysis, BLOCKIN BLOCKIN as BLOCKIN BLOCKIN measures BLOCKIN BLOCKIN of BLOCKIN BLOCKIN dependence BLOCKIN BLOCKIN among BLOCKIN BLOCKIN variables, BLOCKIN BLOCKIN and BLOCKIN BLOCKIN as BLOCKIN BLOCKIN descriptions BLOCKIN BLOCKIN of BLOCKIN BLOCKIN order in biological and physical systems. Information-­‐‑ related m...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

We study the definability of certain subgroups of a group G that does not have the independence property. If a (type) definable subset X of an elementary extension G of G has property P , we call its trace X∩G over G an externally (type) definable P set. We show the following. Centralisers of subsets of G are externally definable subgroups. Cores of externally definable subgroups and iterated c...

The main focus in this work is to establish that L-group theory, which uses the language of functions instead formal set theoretic language, capable capturing most refined ideas and concepts classical group theory. We demonstrate by extending notion subnormality L-setting investigating its properties. develop a mechanism tackle join problem subnormal L-subgroups. conjugate L-subgroup as defined...

We study the quotient of $\mathcal{T}_n = Rep(GL(n|n))$ by tensor ideal negligible morphisms. If we consider full subcategory $\mathcal{T}_n^+$ $\mathcal{T}_n$ indecomposable summands in iterated products irreducible representations up to parity shifts, its is a semisimple tannakian category $Rep(H_n)$ where $H_n$ pro-reductive algebraic group. determine connected derived subgroup $G_n \subset ...