Finite index supergroups and subgroups of torsionfree abelian groups of rank two

Katsuya Eda*, Vlasta Matijević

*この研究の対応する著者

    研究成果: Article査読

    2 被引用数 (Scopus)

    抄録

    Every torsionfree abelian group A of rank two is a subgroup of Q ⊕ Q and is expressed by a direct limit of free abelian groups of rank two with lower diagonal integer-valued 2 × 2-matrices as the bonding maps. Using these direct systems we classify all subgroups of Q ⊕ Q which are finite index supergroups of A or finite index subgroups of A. Using this classification we prove that for each prime p there exists a torsionfree abelian group A satisfying the following, where A ≤ Q ⊕ Q and all supergroups are subgroups of Q ⊕ Q: (1)for each natural number s there are ∑q | s, gcd (p, q) = 1 q s-index supergroups and also ∑q | s, gcd (p, q) = 1 q s-index subgroups;(2)each pair of distinct s-index supergroups are non-isomorphic and each pair of distinct s-index subgroups are non-isomorphic.

    本文言語English
    ページ(範囲)3567-3587
    ページ数21
    ジャーナルJournal of Algebra
    319
    9
    DOI
    出版ステータスPublished - 2008 5 1

    ASJC Scopus subject areas

    • 代数と数論

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