1. Introduction. Let A be the affine building of a simple adjoint algebraic group Q of relative rank > 2 over a locally compact local field K. Let Aut A (resp. E Aut A) denote the group of type-preserving (resp. of all) auto-morphisms of A. Note that E Aut A contains the group $(K) of ÜT-rational points of §. We will be interested in discrete subgroups of Aut A which are chamber-transitive on A...

Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...

Given a smooth projective varietyX , we denote byD(X) the bounded derived category of coherent sheaves D(Coh(X)). All varieties we consider below are over the complex numbers. A result of Rouquier, [Ro] Théoréme 4.18, asserts that if X and Y are smooth projective varieties with D(X) ' D(Y ) (as linear triangulated categories), then there is an isomorphism of algebraic groups Aut(X)× Pic(X) ' Au...

Let G be a finite group. We denote by Γ(G) the prime graph of G. Let S be a sporadic simple group. M. Hagie in (Hagie, M. (2003), The prime graph of a sporadic simple group, Comm. Algebra, 31: 44054424) determined finite groups G satisfying Γ(G) = Γ(S). In this paper we determine finite groups G such that Γ(G) = Γ(A) where A is an almost sporadic simple group, except Aut(McL) and Aut(J2).

We show a result that can be expressed in any of the following three equivalent ways: 1. All self-scaled barrier functionals for the cone + of symmetric positive semideenite matrices are homothetic transformation of the universal barrier functional. 2. All self-scaled barrier functionals for + can be expressed in the form X 7 ! ?c 1 ln det X + c 0 for some constants c 1 > 0; c 0 2 R. 3. All sel...

Given a CAT(0) cube complex X, we show that if Aut(X) 6= Isom(X) then there exists a full subcomplex of X which decomposes as a product with R. As applications, we prove that ifX is δ-hyperbolic, cocompact and 1-ended, then Aut(X) = Isom(X) unless X is quasi-isometric to H, and extend the rank-rigidity result of Caprace–Sageev to any lattice Γ ≤ Isom(X).

For a group $G$ and set $A$, let $\text{End}(A^G)$ be the monoid of all cellular automata over $A^G$, $\text{Aut}(A^G)$ its units. By establishing characterisation surjunctuve groups in terms $\text{End}(A^G)$, we prove that rank (i.e. smallest cardinality generating set) is equal to plus relative latter infinite when has an decreasing chain normal subgroups finite index, condition which satisf...

The present paper deals with the classical results of A. Weil [11] on regularization of pre-groups and pre-transformation spaces (see Definitions 3.1 and 4.1). As pointed out in [4], those purely algebraic results appear to be very useful in the following complex analytic setting. Let D ⊂ C be a bounded domain and Aut(D) the group of all holomorphic automorphisms of D . By a theorem of H. Carta...