Idempotent words in nilpotent groups
Ernest Płonka (1974)
Colloquium Mathematicae
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Ernest Płonka (1974)
Colloquium Mathematicae
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Litvinov, G.L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Kim, Jin Bai, Dowdy, James E. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Robert W. Quackenbush (1974)
Colloquium Mathematicae
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J. Płonka (1970)
Colloquium Mathematicae
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Friedland, Shmuel, Virnik, Elena (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Geok Choo Tan (1997)
Publicacions Matemàtiques
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Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → G where G = inv lim(G/ΓG). Here ΓG is the commutator subgroup [G,G] and ΓG the subgroup [G, ΓG] when i > 2. In this paper, we prove that P-nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with Z coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of...
Peter Šemrl (2007)
Banach Center Publications
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The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver...
Ágnes Szendrei (1996)
Mathematica Slovaca
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H. Wang (1994)
Semigroup forum
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Margalida Mas Grimalt, Joan Torrens, Tomasa Calvo, Marc Carbonell (1999)
Mathware and Soft Computing
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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.