منابع مشابه
Linear equations over finite abelian groups
One of the oldest problems in algebra is the solution of a system of linear equations over certain domains. The Gaussian elimination algorithm provides an effective solution over fields. The Smith normal form algorithm yields a method over the integers. Here we consider another variation of this theme. Let A be a finite (additive) abelian group, let αi,j ∈ End(A) for 1 ≤ i ≤ n and 1 ≤ j ≤ m and...
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Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
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Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of symmetries that can be huge, and the problem of their very existence is NP-hard. We formulate such an existence problem as a constraint problem on one variable (the s...
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Abstract. It is well known (and a result of Goodman) that a random 2-colouring of the edges of a large complete graph Kn contains asymptotically (in n) the minimum number of monochromatic triangles (K3s). Erdős conjectured that a random 2-colouring also minimises the number of monochromatic K4s, but his conjecture was disproved by Thomason in 1989. The question of determining for which small gr...
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We show that for any finitely generated group of matrices that is not virtually solvable, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of at most m generators, such that a and b are free generators of a free subgroup. This uniformity result improves the original statement of the Tits alternative.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1951
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1951-0041137-8