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Groups of finite rank [PDF]

, 1964
We use the following notation and terminology. All groups are written additively. A group is said to be periodic if all its elements are of finite order. As usual, Z stands for the additive group of the integers. The kernel (image) of a homomorphism f is denoted by Ker f (Im f). If H is a normal subgroup of G we write H ⊲ G.
C. R. Curjel, M. Arkowitz
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Elementary Properties of the Finite Ranks

Mathematical Logic Quarterly, 1998
AbstractThis note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first‐order definable over the class of finite directed graphs and that this class admits a first‐order definable global linear order. We apply this last result to show that FO(<, BIT) = FO(BIT).
Dawar, Anuj, Doets, Kees, Lindell, Steven, Weinstein, Scott   +3 more
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SPACES WITH BASES OF FINITE RANK

Mathematics of the USSR-Sbornik, 1972
In this article we investigate spaces having bases of finite rank and finite big rank. Bibliography: 12 items.
V V Filippov, A V Arhangel'skiĭ
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Rank of a finite automaton

Cybernetics and Systems Analysis, 1992
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On groups that are residually of finite rank

Israel Journal of Mathematics, 1998
A group has rank \(r\), \(r\) a positive integer, if every finitely generated subgroup of \(G\) can be generated by \(r\) elements, and if no smaller integer has this property. The authors study groups that are residually of rank \(r\). For example, Theorem 1 states that a periodic group that is residually (locally finite and of rank \(r\)), is locally
Howard Smith, Martin J. Evans, Martyn R. Dixon   +2 more
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Finite rank perturbations of contractions

Integral Equations and Operator Theory, 2000
Let \(T\) be a contraction on an infinite-dimensional complex Hilbert space with finite-dimensional defect spaces \(D_T\) and \(D_{T^*}\). Assume that \(T^{*n}x\to 0\) for any \(x\in H\). \(T\) is then said to be of class \(C_0\). The author studies finite rank perturbations of contractions of class \(C_0\).
Dan Timotin, Chafiq Benhida
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Products of groups with finite rank [PDF]

Archiv der Mathematik, 1987
Das Hauptergebnis ist das folgende Theorem. Die Gruppe \(G=A_ 1...A_ t\) sei das Produkt von endlich vielen paarweise vertauschbaren Untergruppen \(A_ 1,...,A_ t\), von denen t-1 auflösbar sind mit periodischer oder polyzyklischer Hyperzentrumsfaktorgruppe \(A_ i/H(A_ i)\), und sei H ein auflösbarer Normalteiler von G.
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Residually finite groups of finite rank

Mathematical Proceedings of the Cambridge Philosophical Society, 1989
The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters’, show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird.
Alexander Lubotzky, Avinoam Mann
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