منابع مشابه
Boolean Powers of Abelian Groups
where (f + g)(u) = V_,,+,,,f(v) A f(w). Since E is countable, ZcB) can be defined for any countably complete Boolean algebra (ccBa) B where Z is the group of the integers. This kind of group was first (1962) studied by Balcerzyk [l]. However, it seems that not much attention was paid to such groups for a rather long period. Under the point of view in [l, Theorem 51 and [13, Proposition 11, it c...
متن کاملBoolean Powers of Groups
A group is ^-separating if a Boolean power of the group has a unique Boolean algebra. It is proved that a finite subdirectly irreducible group is S-separating if and only if it is non-Abelian. Suppose B is a Boolean ring and G is a group. Let B[G] denote the group ring of G with coefficient ring B. The Boolean power G [B] is defined to be the set of those elements 2e,.g,. EB[G] such that (1) 2e...
متن کاملAbelian Groups Determined by Subgroup Lattices of Direct Powers
In this short note, we show that the class of abelian groups determined by the subgroup lattice of their direct n-powers is exactly the class of the abelian groups which share the n-root property. As applications we answer in the negative a (semi)conjecture of Palfy and solve a more general problem. Recently, for an arbitrary group G, the subgroup lattice of the square G×G has received some att...
متن کاملNon-Boolean Almost Perfect nonlinear Functions on Non-Abelian Groups
The study of nonlinear properties of Boolean functions is one of the major tasks in secret-key cryptography. But the adjective "nonlinear" has several meanings: it can be related to the resistance against the famous differential attack [2] and, in this interpretation, actually refers to (almost) perfect nonlinear functions. Moreover nonlinearity is also related to the maximum magnitude of the F...
متن کاملnon-divisibility for abelian groups
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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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1990
ISSN: 0168-0072
DOI: 10.1016/0168-0072(90)90045-4