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Finite Rank Operators in Certain Algebras
Canadian Mathematical Bulletin, 1999AbstractLet Alg(ℒ) be the algebra of all bounded linear operators on a normed linear space X leaving invariant each member of the complete lattice of closed subspaces L. We discuss when the subalgebra of finite rank operators in Alg(ℒ) is non-zero, and give an example which shows this subalgebra may be zero even for finite lattices.
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On Torsion-Free Groups of Finite Rank
Canadian Journal of Mathematics, 1984This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for ...
Meier, David, Rhemtulla, Akbar
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On Hyper (Abelian of Finite Rank) Groups
Algebra Colloquium, 2008We study the class of groups G, each of whose non-trivial images contains a non-trivial abelian normal subgroup of finite rank. This is very much wider than the class, studied earlier by Robinson and others, of hyperabelian groups H with finite abelian section rank. Our main results are that these groups G are hypercentral by residually finite and are
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Solvable Groups of Finite Metabelian Rank
Siberian Mathematical Journal, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On groups of finite normal rank.
2019A group \(G\) is said to have finite normal rank \(r\) if \(r\) is the minimal number with the property that for any finite set of elements \(g_1,\dots,g_n\) of the group \(G\) there exist elements \(h_1,\dots,h_m\) of \(G\) such that \(m\leq r\) and \(\langle h_1,\dots,h_m\rangle^G=\langle g_1,\dots,g_n\rangle^G\).
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The Rank and Coexponent of a Finite P-Group
Journal of Systems Science and Complexity, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Number of Prolongations of a Finite Rank Valuation
Canadian Journal of Mathematics, 1971A (non-archimedean) valuation v on a field K is said to be henselian if it has a unique prolongation to a valuation on Ka, the algebraic closure of K. A henselization (Kh, vh) of a valuated field (K, v) is a smallest separable extension of K containing a henselian prolongation vh of v.
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