The balanced-projective dimension of abelian $p$-groups
نویسندگان
چکیده
منابع مشابه
A 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...
متن کاملThe computable dimension of ordered abelian groups
Let G be a computable ordered abelian group. We show that the computable dimension of G is either 1 or ω, that G is computably categorical if and only if it has finite rank, and that if G has only finitely many Archimedean classes, then G has a computable presentation which admits a computable basis.
متن کاملFree Topological Groups and the Projective Dimension of a Locally Compact Abelian Group
It is shown that a free topological group on a k.space is a k.-space. Using this it is proved that if X is a k.-group then it is a quotient of a free topological group by a free topological group. A corollary to this is that the projective dimension of any k.-group, relative to the class of all continuous epimorphisms admitting sections, is either zero or one. In particular the projective dimen...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1986
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1986-0814915-0