Displaying similar documents to “The Serre group E 2 p , q ”

On blocks of arithmetic progressions with equal products

N. Saradha (1997)

Journal de théorie des nombres de Bordeaux

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Let f ( X ) ∈ ℚ [ X ] be a monic polynomial which is a power of a polynomial g ( X ) ∈ ℚ [ X ] of degree μ ≥ 2 and having simple real roots. For given positive integers d 1 , d 2 , ℓ , m with ℓ < m and gcd ( ℓ , m ) = 1 with μ ≤ m + 1 whenever m < 2 , we show that the equation f ( x ) f ( x + d 1 ) ⋯ f ( x + ( ℓ k - 1 ) d 1 ) = f ( y ) f ( y + d 2 ) ⋯ f ( y + ( m k - 1 ) d 2 ) with f ( x + j d 1 ) ≠ 0 for 0 ≤ j < ℓ k has only finitely many solutions in integers x , y and k ≥ 1 except in the case m = μ = 2 , ℓ = k = d 2 = 1 , f ( X ) = g ( X ) , x = f ( y ) + y .

Non-free two-generator subgroups of SL(Q).

S. Peter Farbman (1995)

Publicacions Matemàtiques

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The question of whether two parabolic elements A, B of SL(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL(C) will not be free.

Galois covers between K 3 surfaces

Gang Xiao (1996)

Annales de l'institut Fourier

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We give a classification of finite group actions on a K 3 surface giving rise to K 3 quotients, from the point of view of their fixed points. It is shown that except two cases, each such group gives rise to a unique type of fixed point set.