We analyze K3 surfaces admitting an elliptic fibration E and a finite group G of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration E/G comparing its properties to the ones of E. We show that if E admits an n-torsion section, its quotient by the group of automorphisms induced by this section admits again an n-torsion section. Considering au...

Rational automorphisms of products of simple p-compact groups are shown to be composites of products of rational automorphisms of the individual factors and permutation maps.

We prove induced Ramsey theorems in which the induced monochromatic subgraph satisfies that some of its partial automorphisms extend to automorphisms of the colored graph.

We classify the group of birational automorphisms Hilbert schemes points on algebraic K3 surfaces Picard rank one. study whether these are symplectic or non-symplectic and if there exists a hyperkähler model which they become biregular. also present new geometrical constructions for some automorphisms.

A finite group amalgam of index (k,m) is a 5-tuple (L,φ,B, ψ,R) where L, B, and R are finite groups, φ : B → L and ψ : B → R are monomorphisms, and the indices of B and B in L and R are k and m, respectively. The amalgam is faithful if N ≤ B, N C L, and N C R implies N = 1. It is well known that the finite faithful amalgams of index (k, 2) are in a bijective correspondence with (the conjugacy c...

In this paper, we study a flag complex which is naturally associated to the Thurston theory of surface diffeomorphisms for compact connected orientable surfaces with boundary [21]. The various pieces of the Thurston decomposition of a surface diffeomorphism, thick domains and annular or thin domains, fit into this flag complex, which we call the complex of domains. The main result of this paper...

Abstract A rigid automorphism of a linking system is an that restricts to the identity on Sylow subgroup. inner conjugation by element in center At odd primes, it known each centric inner. We prove group outer automorphisms at prime $2$ elementary abelian and splits over subgroup automorphisms. In second result, we show if finite G for , then $p'$ -order modulo automorphisms, provided has no no...

Using the Kramer-Mesner method, 4-(26, 6, λ) designs with PSL(2, 25) as a group of automorphisms and with λ in the set {30, 51, 60, 81, 90, 111} are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called “quasi-designs”. Actions of groups PSL(2, 25), PGL(2, 25) and twisted PGL(2, 25) are being compared. It is shown that there exist 4-(2...