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Displaying similar documents to “Invariance of the parity conjecture for p -Selmer groups of elliptic curves in a D 2 p n -extension”

Thompson’s conjecture for the alternating group of degree 2 p and 2 p + 1

Azam Babai, Ali Mahmoudifar (2017)

Czechoslovak Mathematical Journal

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For a finite group G denote by N ( G ) the set of conjugacy class sizes of G . In 1980s, J. G. Thompson posed the following conjecture: If L is a finite nonabelian simple group, G is a finite group with trivial center and N ( G ) = N ( L ) , then G L . We prove this conjecture for an infinite class of simple groups. Let p be an odd prime. We show that every finite group G with the property Z ( G ) = 1 and N ( G ) = N ( A i ) is necessarily isomorphic to A i , where i { 2 p , 2 p + 1 } .

The local lifting problem for actions of finite groups on curves

Ted Chinburg, Robert Guralnick, David Harbater (2011)

Annales scientifiques de l'École Normale Supérieure

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Let k be an algebraically closed field of characteristic p > 0 . We study obstructions to lifting to characteristic 0 the faithful continuous action φ of a finite group G on k [ [ t ] ] . To each such  φ a theorem of Katz and Gabber associates an action of G on a smooth projective curve Y over k . We say that the KGB obstruction of φ vanishes if G acts on a smooth projective curve X in characteristic  0 in such a way that X / H and Y / H have the same genus for all subgroups H G . We determine for which G the KGB...

An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel (2014)

Journal de Théorie des Nombres de Bordeaux

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Let C be a hyperelliptic curve of genus g 1 over a number field K with good reduction outside a finite set of places S of K . We prove that C has a Weierstrass model over the ring of integers of K with height effectively bounded only in terms of g , S and K . In particular, we obtain that for any given number field K , finite set of places S of K and integer g 1 one can in principle determine the set of K -isomorphism classes of hyperelliptic curves over K of genus g with good reduction outside...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

A variation of Thompson's conjecture for the symmetric groups

Mahdi Abedei, Ali Iranmanesh, Farrokh Shirjian (2020)

Czechoslovak Mathematical Journal

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Let G be a finite group and let N ( G ) denote the set of conjugacy class sizes of G . Thompson’s conjecture states that if G is a centerless group and S is a non-abelian simple group satisfying N ( G ) = N ( S ) , then G S . In this paper, we investigate a variation of this conjecture for some symmetric groups under a weaker assumption. In particular, it is shown that G Sym ( p + 1 ) if and only if | G | = ( p + 1 ) ! and G has a special conjugacy class of size ( p + 1 ) ! / p , where p > 5 is a prime number. Consequently, if G is a centerless group with N ( G ) = N ( Sym ( p + 1 ) ) , then...

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

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In this paper we prove the following theorems in incidence geometry. 1. There is δ > 0 such that for any P 1 , , P 4 , and Q 1 , , Q n 2 , if there are n ( 1 + δ ) / 2 many distinct lines between P i and Q j for all i , j , then P 1 , , P 4 are collinear. If the number of the distinct lines is < c n 1 / 2 then the cross ratio of the four points is algebraic. 2. Given c > 0 , there is δ > 0 such that for any P 1 , P 2 , P 3 2 noncollinear, and Q 1 , , Q n 2 , if there are c n 1 / 2 many distinct lines between P i and Q j for all i , j , then for any P 2 { P 1 , P 2 , P 3 } , we have δ n distinct lines between P and Q j . 3. Given...