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Rendiconti del Circolo Matematico di Palermo, 1980
An investigation into an algebraic system with a single binary operation, called a skew-group, based on axioms of associativity; skew-commutativity (x+y+z=x+z+y); right identity; and left inverse. Definitions are given for left coset, quotient skew-group, homorphism, kernel, and subnormal skew-subgroup.
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An investigation into an algebraic system with a single binary operation, called a skew-group, based on axioms of associativity; skew-commutativity (x+y+z=x+z+y); right identity; and left inverse. Definitions are given for left coset, quotient skew-group, homorphism, kernel, and subnormal skew-subgroup.
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Russian Academy of Sciences. Sbornik Mathematics, 1993
Let \(V\) be a set of (finite) words in an alphabet of variables ranging over elements of a group \(G\). The subgroup \(V(G)\) of the group \(G\) generated by all values of words from \(V\) is called the verbal subgroup defined by the set \(V\). The width of the subgroup \(V(G)\) is defined to be the minimal number \(m \in \mathbb{N} \cup \{+\infty\}\)
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Let \(V\) be a set of (finite) words in an alphabet of variables ranging over elements of a group \(G\). The subgroup \(V(G)\) of the group \(G\) generated by all values of words from \(V\) is called the verbal subgroup defined by the set \(V\). The width of the subgroup \(V(G)\) is defined to be the minimal number \(m \in \mathbb{N} \cup \{+\infty\}\)
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2018
The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's ...
Druţu, C, Kapovich, M
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The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's ...
Druţu, C, Kapovich, M
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Noûs, 2017
AbstractA group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever ...
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AbstractA group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever ...
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The Theory of Proportionality as an Abstraction of Group Theory
Mathematische Annalen, 1955Die Verff. zeigen, daß die Permutation \(\sigma\) der Elemente der Gruppe \(G\) dann und nur dann dem Holomorph von \(G\) angehört, wenn \(\sigma\) die Proportionalitätsrelation \(ab^{-1}=cd^{-1}\) invariant läßt. Weiter geben Verff. eine axiomatische Charakterisierung dieser vierstelligen Proportionalitätsrelation.
Büchi, J. Richard, Wright, Jesse B.
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Appreciative Remarks on the Theory of Groups.
The Mathematical Gazette, 1903While it is clearly impossible for the average high school teacher of mathematics to become familiar with all the modern branches of this subject, it is desirable that he should not be totally ignorant of any extensive branch. The views of a number of eminent mathematicians often furnish one of the simplest as well as one of the most reliable ...
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2010
Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications.
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Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications.
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