Except for a set of first category, all pairs of measure preserving transformations generate a dense subgroup of G, the group of all invertible measure preserving transformations of the unit interval when G has the weak topology. Consider G the group of invertible (Lebesgue) measure preserving transformations of the unit interval onto itself. On G, we put the weak topology (Halmos [2, pp. 61-67...

Tumour necrosis factor (TNF)-alpha is known to play a major role in the formation of noncaseating granuloma, a hallmark of sarcoidosis. The main cellular source in situ is still ambiguous. Serial sections of transbronchial biopsies from 14 patients with and 12 without sarcoidosis were studied, using immunohistochemistry (IHC), for TNF-alpha, T-cells (CD3), macrophages (CD68), and epithelial cel...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal{h}$-subgroup in‎ ‎$g$ if $n_g(h)cap h^{g}leq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ ‎$mathcal{h}^{ast}$-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal{h}$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎as...

Kulikov has exhibited an étale morphism F : X → Cn of degree d > 1 which is surjective modulo codimension two with X simply connected, settling his generalized jacobian problem. His method reduces the problem to finding a hypersurface D ⊂ Cn and a subgroup G ⊂ π1(C − D) of index d generated by geometric generators. By contrast we show that if D has simple normal crossings away from a set of cod...

Let X be a connected locally finite graph with vertex-transitive automorphism group. If X has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup of AUT(X) and the action of AUT(X) on V(X) is imprimitive if X is not finite. If X has infinitely many ends, the group of bounded automorphisms itself is locally finite and periodic.

Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties X w̃ (bσ) of a quasisplit connected reductive group G over F = Fq((t)) for a parahoric subgroup P . They asked which pairs (b, w̃) give non-empty varieties, and in these cases what dimensions do these varieties have. This paper answers these questions for P = I an Iwahori subgroup, in the cases b = 1, G = SL2, SL3, Sp4. This infor...

A century ago, Camille Jordan proved that the complex general linear group GLn(C) has the Jordan property: there is a Jordan constant Cn such that every finite subgroup H ≤ GLn(C) has an abelian subgroup H1 of index [H : H1] ≤ Cn. We show that every connected algebraic group G (which is not necessarily linear) has the Jordan property with the Jordan constant depending only on dimG, and that the...

Let G be a finite group. A coprime commutator in is any element that can written as [x,y] for suitable x,y∈G such π(x)∩π(y)=∅. Here π(g) denotes the set of prime divisors order g∈G. An anti-coprime an [x,y], where π(x)=π(y). The main results paper are follows. If |xG|≤n whenever x commutator, then has nilpotent subgroup n-bounded index. every x∈G, H nilpotency class at most 4 [G:H] and |γ4(H)| ...

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |XXX|/|X| bounded is close to a finite subgroup, or else to a subset of a proper algebraic subgroup of G. We also find a connection with Lie groups, and use it to obtain some consequences s...

Let R be a ring with unity and U(R) its group of units. Let ∆U = {a ∈ U(R) | [U(R) : CU(R)(a)] < ∞} be the FC-radical of U(R) and let ∇(R) = {a ∈ R | [U(R) : CU(R)(a)] < ∞} be the FC-subring of R. An infinite subgroup H of U(R) is said to be an ω-subgroup if the left annihilator of each nonzero Lie commmutator [x, y] in R contains only finite number of elements of the form 1− h, where x, y ∈ R ...