On a certain purification problem for primary abelian groups
نویسندگان
چکیده
منابع مشابه
non-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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On a Permutation Problem for Finite Abelian Groups
LetG be a finite additive abelian group with exponent n > 1, and let a1, . . . , an−1 be elements of G. We show that there is a permutation σ ∈ Sn−1 such that all the elements saσ(s) (s = 1, . . . , n− 1) are nonzero if and only if ∣∣∣{1 6 s < n : n d as 6= 0 }∣∣∣ > d− 1 for every positive divisor d of n. When G is the cyclic group Z/nZ, this confirms a conjecture of Z.-W. Sun.
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It is proved that if A is an abelian p-group with a pure subgroup G so that A/G is at most countable and G is either p-totally projective or p-summable, then A is either p-totally projective or p-summable as well. Moreover, if in addition G is nice in A, then G being either strongly p-totally projective or strongly p-summable implies that so is A. This generalizes a classical result of Wallace ...
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In this note, we define the class of finite groups of Suzuki type, which are non–abelian groups of exponent 4 and class 2 with special properties. A group G of Suzuki type with |G| = 22s always possesses a non–trivial difference set. We show that if s is odd, G possesses a central difference set, whereas if s is even, G has no non–trivial central difference set.
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 1966
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.1639