Let G be a connected reductive algebraic group over Fp and let F : G → G be a Frobenius endomorphism endowing G with an Fq-rational structure. Bonnafé–Michel have shown that the Mackey formula for Deligne–Lusztig induction and restriction holds for the pair (G, F) except in the case where q = 2 and G has a quasi-simple component of type E6, E7, or E8. Using their techniques we show that if q = ...

We obtain a description of quasi-endomorphism rings torsion-free Abelian groups G rank 4, quasi-decomposable into direct sum A1 and A2 1 strongly indecomposable group B 2 in the case where quasi-homomorphism ℚ ⨂ Hom(A2,B) has 2.

It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...

Proposition 1.1. Let f : R1 → R2 be a homomorphism of rings. If J is an ideal of R2, then f (J) is an ideal of R1 containing ker(f) and furthermore f(f(J)) ⊆ J . Now let f : R1 → R2 be an epimorphism of rings. If J is an ideal of R2 then f(f (J)) = J . If I is an ideal of R1 then f(I) is an ideal of R2. Furthermore we have I ⊆ f (f(I)) = I + ker(f) and thus I = f(f(I)) if I contains ker(f). Thu...

We introduce a new class of graphs which we call P3-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P3-dominated graph. We prove that G is hamiltonian if α(G) ≤ κ(G), with two exceptions: K2,3 and K1,1,3. We also prove that G is hamiltonian if G is 3-connected and |V (G)| ≤ 5δ(G) − 5. These results extend known re...

In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter T (E) = P (E,Ω) + G (E) with a volume constraint. Here Ω is any open subset of Rn with n ≥ 2, G is a lower semicontinuous function on sets of finite perimeter satisfying a condition that G (E) ≤ G (F ) + C |E∆F | among all sets of finite perimeter with equal volume. We show that under the condition β >...

Let G be a group and let k > 2 be an integer, such that (A: — 3)(A: — 1) < |G|/15 if G is finite. Suppose that the condition \A\ < k(k+l)/2 + (k-'i)/2 is satisfied by every it-element subset A c G. Then G is abelian. The proof uses the structure of quasi-invariant sets.

Preface The main goal of this book is to describe several tools of the quasi-isometric rigidity and to illustrate them by presenting (essentially self-contained) proofs of several fundamental theorems in this area: Gromov's theorem on groups of polynomial growth, Mostow Rigidity Theorem and Schwartz's quasi-isometric rigidity theorem for nonuniform lattices in the real-hyperbolic spaces. We con...

An inverse coefficient problem related to identification of the plasticity function g(η) from a given torque τ is studied for a circular section bar. Within the deformation theory of plasticity the mathematical model of torsion leads to the nonlinear Dirichlet problem −∇ · (g(|∇u|2)∇u) = 2φ, x ∈ Ω ⊂ R2; u(s) = 0, s ∈ ∂Ω . For determination of the unknown coefficient g(η) ∈ G, an integral of the...