Displaying similar documents to “О p -группах автоморфизмов абелевых p -групп”

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths

Weidong Gao, Yuanlin Li, Pingping Zhao, Jujuan Zhuang (2016)

Colloquium Mathematicae

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Let G be an additive finite abelian group. For every positive integer ℓ, let d i s c ( G ) be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine d i s c ( G ) for certain finite groups, including cyclic groups, the groups G = C C 2 m and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum...

On the Davenport constant and group algebras

Daniel Smertnig (2010)

Colloquium Mathematicae

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For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence S = g · . . . · g l over G such that ( X g - a ) · . . . · ( X g l - a l ) 0 K [ G ] for all a , . . . , a l K × . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for...

Deformation theory and finite simple quotients of triangle groups I

Michael Larsen, Alexander Lubotzky, Claude Marion (2014)

Journal of the European Mathematical Society

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Let 2 a b c with μ = 1 / a + 1 / b + 1 / c < 1 and let T = T a , b , c = x , y , z : x a = y b = z c = x y z = 1 be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of T ? (Classically, for ( a , b , c ) = ( 2 , 3 , 7 ) and more recently also for general ( a , b , c ) .) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially...

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

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The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age 1 . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....