Let G be a group and H subgroup of G. The notion being hyperbolically embedded in was introduced by Dahmani, Guiraldel, Osin. This note introduces an equivalent definition hyperbolic based on Bowditch’s approach to relatively groups terms fine graphs.

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a no...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

Let G be a finite subgroup of a symplectic group Sp2d(Ql). Despite the fact ([3]) that G can fail to be conjugate in GL2d(Ql) to a subgroup of Sp2d(Zl), we prove that it can nevertheless be embedded in Sp2d(Fl) in such a way that the characteristic polynomials are preserved (mod l), as long as l > 3. We start with the following “rigidity” result, which is in the spirit of similar results by Min...

We study the Newman--Unti (NU) group from viewpoint of infinite-dimensional geometry. The NU is a topological in natural coarse topology, but it does not become manifold and hence Lie this topology. To obtain structure we consider finer Whitney-type This turns unit component into an group. then theoretic properties Surprisingly, operations full discontinuous, whence support structure. contains ...

a novel zinc oxide - agar nanocomposite was successfully synthesized using zinc chloride as a precursor. the nanocomposite was prepared using a domestic microwave oven. the prepared nanocomposites have been characterized by fourier transform infrared (ftir) spectroscopy, x-ray diffraction (xrd) analysis, scanning electron microscopy (sem) and uv- visible spectroscopy. the crystalline properties...

An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...

For a prime p, a proper subgroup H of the finite group G is strongly p-embedded in G if p divides |H| and p does not divide |H ∩ H| for all g ∈ G \H . A characteristic property of strongly p-embedded subgroups is that NG(X) ≤ H for any non-trivial p-subgroup X of H . Strongly p-embedded subgroups appear in the final stages of one of the programmes to better understand the classification of the ...

Let L be a simply-connected simple connected algebraic group over number field F, and H semisimple absolutely maximal F-subgroup of L. $$\Delta (H)$$ the image diagonally embedded in $$L^n$$ . Under cohomological condition, we prove an asymptotic formula for rational points bounded height on projective equivariant compactifications (H)\backslash L^n$$ with respect to balanced line bundle.