Dimension and lower central subgroups of metabelian p-groups
نویسندگان
چکیده
منابع مشابه
Subgroups 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...
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1.1. Baumslag's theorem has another facet. It shows that in the variety 2l of metabelian groups, every finitely generated $I-group G occurs as a subgroup of some finitely presented 2I-group G. The analogous result for the variety of all groups is a celebrated theorem of G. Higman [8] which states that a finitely generated group G is the subgroup of a finitely presented group G if, and only if, ...
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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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Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...
متن کامل∀-Free Metabelian Groups
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1985
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000000258