Results 301 to 310 of about 6,200,949 (317)
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Communications in Algebra, 2002
We prove that the simple group which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, which has order 979200, whose efficiency or otherwise remains to be determined.
Campbell, C. M. +3 more
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We prove that the simple group which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, which has order 979200, whose efficiency or otherwise remains to be determined.
Campbell, C. M. +3 more
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On simple groups and simple singularities
Israel Journal of Mathematics, 2001Let \(G\) be a simply-connected simple Chevalley group of type \(A\), \(D\) or \(E\) and \(k\) an algebraically closed field whose characteristic is very good for \(G\). According to a conjecture of Grothendieck a semi-universal deformation (also known as miniversal deformation) of the rational double point of the same type can be obtained via a ...
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Scientific American, 2008
The article discusses group theory as it relates to puzzles like Rubik's Cube, which is based on permutation groups, and other types of puzzles the authors invented, based on other sporadic simple groups, including Mathieu groups. Strategies for solving these puzzles are discussed, with sidebars discussing and illustrating group theory.
Paul Siegel, Igor Kriz
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The article discusses group theory as it relates to puzzles like Rubik's Cube, which is based on permutation groups, and other types of puzzles the authors invented, based on other sporadic simple groups, including Mathieu groups. Strategies for solving these puzzles are discussed, with sidebars discussing and illustrating group theory.
Paul Siegel, Igor Kriz
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Non-simple groups which are the product of simple groups
Archiv der Mathematik, 1989This paper investigates the structure of groups with non-trivial center which can be written as a product of two simple subgroups. Examples must be covering groups of simple groups. For example \(2\cdot PSU(4,3)=AB\) where \(A\simeq PSp(4,3)\) and \(B\simeq PSL(4,3)\) and \(3\cdot PSU(4,3)=AB\) where \(A\simeq PSp(4,3)\) and \(B\simeq PSU(3,3).\) The ...
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Canadian Journal of Mathematics, 1962
The list of known finite simple groups other than the cyclic, alternating, and Mathieu groups consists of the classical groups which are (projective) unimodular, orthogonal, symplectic, and unitary groups, the exceptional groups which are the direct analogues of the exceptional Lie groups, and certain twisted types which are constructed with the aid of
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The list of known finite simple groups other than the cyclic, alternating, and Mathieu groups consists of the classical groups which are (projective) unimodular, orthogonal, symplectic, and unitary groups, the exceptional groups which are the direct analogues of the exceptional Lie groups, and certain twisted types which are constructed with the aid of
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On characteristically simple groups
Mathematical Proceedings of the Cambridge Philosophical Society, 19761ยท1. A group is called characteristically simple if it has no proper non-trivial subgroups which are left invariant by all of its automorphisms. One familiar class of characteristically simple groups consists of all direct powers of simple groups: this contains all finite characteristically simple groups, and, more generally, all characteristically ...
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Journal of the London Mathematical Society, 1995
A group \(G\) is called pseudofinite if it is an infinite model of the first-order theory of finite groups. The study of these groups was begun in 1988 by the reviewer who realized, that a classification of all simple pseudofinite groups might be possible.
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A group \(G\) is called pseudofinite if it is an infinite model of the first-order theory of finite groups. The study of these groups was begun in 1988 by the reviewer who realized, that a classification of all simple pseudofinite groups might be possible.
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A characteristically simple group
Mathematical Proceedings of the Cambridge Philosophical Society, 1954The object of this note is to give an example of an infinite locally finite p-group which has no proper characteristic subgroup except the unit group. (A group G is a locally finite p-group if every finite set of elements of G generates a subgroup of finite order equal to a power of the prime p.) It is known that an infinite locally finite p-group ...
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The Classification of the Finite Simple Groups
The Mathematical Intelligencer, 1980This article on the classification of finite simple groups is directed towards a broad audience. The author poses some natural questions connected with finite groups and in particular with finite simple groups. He explains in a lucid way why these questions have particular answers.
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