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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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Journal of the London Mathematical Society, 1968
Publisher Summary This chapter describes the group theory. The theory of groups and its close relatives include such a wide range of mathematics that it is necessary to make some subdivision to be able to describe its present state. A group is said to be simple if, apart from itself and the trivial group, it has no normal subgroups.
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Publisher Summary This chapter describes the group theory. The theory of groups and its close relatives include such a wide range of mathematics that it is necessary to make some subdivision to be able to describe its present state. A group is said to be simple if, apart from itself and the trivial group, it has no normal subgroups.
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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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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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Cybernetics, 1969
Summary: In this paper the error correcting possibilities of cyclic codes are studied and the more general class of abelian codes is introduced. The well known Reed-Muller codes are also a particular case of abelian codes. The methods of the theory of finite group representations is used for the study of abelian codes.
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Summary: In this paper the error correcting possibilities of cyclic codes are studied and the more general class of abelian codes is introduced. The well known Reed-Muller codes are also a particular case of abelian codes. The methods of the theory of finite group representations is used for the study of abelian codes.
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2013
Contents The elements of group theory 283 Example 32.1: Showing that symmetry operations form a group 284 Brief illustration 32.1: Classes 284 Matrix representations 285 Representatives of operations 285 Brief illustration 32.2 ...
Peter Atkins +2 more
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Contents The elements of group theory 283 Example 32.1: Showing that symmetry operations form a group 284 Brief illustration 32.1: Classes 284 Matrix representations 285 Representatives of operations 285 Brief illustration 32.2 ...
Peter Atkins +2 more
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Oberwolfach Reports, 2012
This was the seventh workshop on Computational Group Theory. It showed that Computational Group Theory has significantly expanded its range of activities. For example, symbolic computations with groups and their representations and computations with infinite groups play a major role nowadays.
Gerhard Hiß +3 more
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This was the seventh workshop on Computational Group Theory. It showed that Computational Group Theory has significantly expanded its range of activities. For example, symbolic computations with groups and their representations and computations with infinite groups play a major role nowadays.
Gerhard Hiß +3 more
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Representation Theory of Groups
2018Representation theory is an important pillar of the group theory. As we shall see soon, a word “representation” and its definition sound a bit daunting.
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