On properties of n-totally projective Abelian p-groups
نویسندگان
چکیده
منابع مشابه
On Extensions of Primary Almost Totally Projective Abelian Groups
Suppose G is a subgroup of the reduced abelian p-group A. The following two dual results are proved: (∗) If A/G is countable and G is an almost totally projective group, then A is an almost totally projective group. (∗∗) If G is countable and nice in A such that A/G is an almost totally projective group, then A is an almost totally projective group. These results somewhat strengthen theorems du...
متن کاملA NOTE ON THE COUNTABLE EXTENSIONS OF SEPARABLE p–PROJECTIVE ABELIAN p–GROUPS
Throughout this brief note all groups are assumed to be abelian p-primary, written additively as is customary when regarding the group structure. Since we shall deal exclusively only with p-torsion abelian groups, for some arbitrary but a fixed prime p, there should be no confusion in future removing the phrase ”is an abelian p-group”. Concerning the terminology, under the term a separable grou...
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We define and investigate the class of almost ω1-n-simply presented p-torsion abelian groups, which class properly contains the subclasses of almost n-simply presented groups and ω1-n-simply presented groups, respectively. The obtained results generalize those obtained by us in Korean J. Math. (2014) and J. Algebra Appl. (2015).
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Let R be a commutative unitary ring of prime characteristic p and G an Abelian p-group such that G ω+n is either torsion-complete or totally projective and G/G ω+n is p-projective. We prove that the group algebra RG over R determines up to isomorphism G, that is, if RH and RG are isomorphic as R-algebras for another group H then H is isomorphic to G. This extends classical results due to May Pr...
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.
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2012
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-012-0685-2