Results 271 to 280 of about 1,276,041 (313)
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Products of Commutators in Free Products
International Journal of Algebra and Computation, 1997The genus of an element in the commutator subgroup of a group \(G\) is the minimal number of commutators of which the element is a product. It has been shown previously that in a free group each element of genus \(n\) can be obtained by permutation and suitable substitution on one of a finite number of words called orientable forms of genus \(n\).
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1993
Recall from Chapter 1 that a group is free if it has a presentation with no non-trivial relations. By Corollary 1.1.6 (c) every group is the homomorphic image of a free group and this indicates the central role that free groups play in combinatorial group theory.
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Recall from Chapter 1 that a group is free if it has a presentation with no non-trivial relations. By Corollary 1.1.6 (c) every group is the homomorphic image of a free group and this indicates the central role that free groups play in combinatorial group theory.
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2004
Among the pathomechanisms involved with traumatic brain and spinal cord injury, reactive oxygen species and lipid peroxidation play an important role [3,4]. In a model of global cerebral ischemia, Baiping and colleagues [1] reported that moderate hypothermia (30°–32°C) attenuated lipid peroxidation.
Nariyuki Hayashi, Dalton W. Dietrich
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Among the pathomechanisms involved with traumatic brain and spinal cord injury, reactive oxygen species and lipid peroxidation play an important role [3,4]. In a model of global cerebral ischemia, Baiping and colleagues [1] reported that moderate hypothermia (30°–32°C) attenuated lipid peroxidation.
Nariyuki Hayashi, Dalton W. Dietrich
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Free Products of Pseudocomplemented Semilattices
Semigroup Forum, 2000Let \({\mathcal K}\) be the variety of pseudocomplemented semilattices (PCSs in brief), let \(S\), \(S_i\in{\mathcal K}\), for \(i\in I\). Then \(S\) is a free product of \(S_i\) \((i\in I)\) if there exist embeddings \(\varphi_i: S_i\to S\) such that \(S\) is generated by the set \(\bigcup \{\varphi_i(S_i);\;i\in I\}\), and if \(T\in K\) and \(\psi_i ...
Katriňák, T., Heleyová, Z.
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1995
The notion of generators and relations can be extended from abelian groups to arbitrary groups once we have a nonabelian analogue of free abelian groups. We use the property appearing in Theorem 10.11 as our starting point.
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The notion of generators and relations can be extended from abelian groups to arbitrary groups once we have a nonabelian analogue of free abelian groups. We use the property appearing in Theorem 10.11 as our starting point.
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Free Products of C ∗ -Algebras
Transactions of the American Mathematical Society, 1982Small ("spatial") free products of C*-algebras are constructed. Under certain conditions they have properties similar to those proved by Paschke and Salinas for the algebras C,*(GI * G2) where G1, G2 are discrete groups. The freeproduct analogs of noncommutative Bernoulli shifts are discussed. 0. Introduction. Let K be a field. Consider the category of
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2011
Finding dilations of Markov semigroups to cocycle perturbations of noises is a fundamental problem of quantum probablity and quantum dynamics. A noise is hereby a reversible quantum dynamics with a filtration that is independent in some notion of quantum independence. The noise is a dilation of the trivial Markov semigroup; the scope is turning it into
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Finding dilations of Markov semigroups to cocycle perturbations of noises is a fundamental problem of quantum probablity and quantum dynamics. A noise is hereby a reversible quantum dynamics with a filtration that is independent in some notion of quantum independence. The noise is a dilation of the trivial Markov semigroup; the scope is turning it into
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1974
A comparative study which contrasts the theory of free groups with the theory of free products has some general interest. One area where comparison can sometimes be made in an elementary way concerns relations, and their consequences: for example, the consequences of the relation XY = YX .
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A comparative study which contrasts the theory of free groups with the theory of free products has some general interest. One area where comparison can sometimes be made in an elementary way concerns relations, and their consequences: for example, the consequences of the relation XY = YX .
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Multidisciplinary standards of care and recent progress in pancreatic ductal adenocarcinoma
Ca-A Cancer Journal for Clinicians, 2020Aaron J Grossberg +2 more
exaly