منابع مشابه
∀-Free Metabelian Groups
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متن کاملOn Embedding of Partially Commutative Metabelian Groups to Matrix Groups
The Magnus embedding of a free metabelian group induces the embedding of partially commutative metabelian group SΓ in a group of matrices MΓ. Properties and the universal theory of the group MΓ are studied.
متن کاملSubgroups of Free Metabelian Groups
In 1954 A. G. Howson proved that the intersection of two finitely generated subgroups of a free group is again finitely generated. Now the free metabelian subgroups of a free metabelian group of finite rank n are quite restricted. Indeed they are again of finite rank at most n. This suggests that there may be an analog of Howson’s theorem for free metabelian groups. This turns out not to be the...
متن کاملImproving tameness for metabelian groups
We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. More generally, we prove that if n is a positive integer and Q is a finitely generated abelian group, then any finitely generated ZQ-module can be embedded in a module that is n-tame. Combining with standard facts, the F3 embedding theorem follows from this and a recent theorem of R. Bieri and...
متن کاملA Construction of Metabelian Groups
In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order p 22 tends to infinity with p. More precisely, for each prime number p there is a family (M λ) λ=0,... ,p−1 of indecom-posable and pairwise nonisomorphic metabelian p-groups of the given order. In this manuscript we use recent results on the classification of possible embeddings of a ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1968
ISSN: 0004-9735
DOI: 10.1017/s1446788700004675