منابع مشابه
Abelian p-groups and the Halting problem
We investigate which effectively presented abelian p-groups are isomorphic relative to the halting problem. The standard approach to this and similar questions uses the notion of ∆2-categoricity (to be defined). We partially reduce the description of ∆ 0 2-categorical p-groups of Ulm type 1 to the analogous problem for equivalence structures. Using this reduction, we solve to a problem left ope...
متن کاملFinite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
متن کاملTHE STRUCTURE OF FINITE ABELIAN p-GROUPS BY THE ORDER OF THEIR SCHUR MULTIPLIERS
A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.
متن کاملThe sum-capture problem for abelian groups
Let G be a finite abelian group, let 0 < α < 1, and let A ⊆ G be a random set of size |G|. We let μ(A) = max B,C:|B|=|C|=|A| |{(a, b, c) ∈ A×B × C : a = b+ c}|. The issue is to determine upper bounds on μ(A) that hold with high probability over the random choice of A. Mennink and Preneel [4] conjecture that μ(A) should be close to |A| (up to possible logarithmic factors in |G|) for α ≤ 1/2 and ...
متن کاملGrowing forests in abelian p-groups
At the center of the theory of abelian p-groups are the classical theorems of Ulm, Zippin and Kaplansky, going back to the thirties, that classify countable p-groups by their Ulm invariants: the uniqueness theorem is referred to as Ulm's theorem, the existence theorem as Zippin's theorem. For each ordinal , the -th Ulm invariant of G can be de ned as the dimension fG( ) of the vector space (ove...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2016
ISSN: 0168-0072
DOI: 10.1016/j.apal.2016.04.016