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...

Let p be an odd prime number and F a field containing a primitive pth root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group GF of F . Namely, the third subgroup G (3) F in the descending p-central sequence of GF is the intersection of all open normal subgroups N such that GF /N is 1, Z/p , or the modular group Mp3 of order p .

Let p be an odd prime number and F a field containing a primitive pth root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group GF of F . Namely, the third subgroup G (3) F in the descending p-central sequence of GF is the intersection of all open normal subgroups N such that GF /N is 1, Z/p , or the extra-special group Mp3 of order p and exponent p.

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.

Cycle sets are known to give non-degenerate unitary solutions of the Yang--Baxter equation and linear cycle enriched versions these algebraic systems. The paper explores recently developed cohomology extension theory for sets. We derive a four term exact sequence relating 1-cocycles, second certain groups automorphisms arising from central extensions This is an analogue similar group due Wells....

Five consecutive bronchopleural fistulas (BPFs) were successfully treated by injecting absolute ethanol directly into the submucosal layer of the fistula under flexible bronchoscopic observation. No complications occurred as a result of this treatment. Our nonsurgical treatment may be very useful to reduce the costs of and duration of hospitalization and to improve the patient's quality of life...

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.

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...