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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 ...
D. H. McLain
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Communications in Algebra, 2002
We prove that the simple group L-3(5) which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, S-4(4) 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 L-3(5) which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, S-4(4) which has order 979200, whose efficiency or otherwise remains to be determined.
Campbell, C. M. +3 more
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On Intermediate Subalgebras of C*-simple Group Actions
International mathematics research notices, 2018We show that for a large class of actions $\Gamma \curvearrowright \mathcal{A}$ of $C^*$-simple groups $\Gamma $ on unital $C^*$-algebras $\mathcal{A}$, including any non-faithful action of a hyperbolic group with trivial amenable radical, every ...
Tattwamasi Amrutam
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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.
Igor, Kriz, Paul, Siegel
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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.
Igor, Kriz, Paul, Siegel
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International Journal of Computer Vision, 2018
Batch Normalization (BN) is a milestone technique in the development of deep learning, enabling various networks to train. However, normalizing along the batch dimension introduces problems—BN’s error increases rapidly when the batch size becomes smaller,
Yuxin Wu, Kaiming He
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Batch Normalization (BN) is a milestone technique in the development of deep learning, enabling various networks to train. However, normalizing along the batch dimension introduces problems—BN’s error increases rapidly when the batch size becomes smaller,
Yuxin Wu, Kaiming He
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The American Mathematical Monthly, 2020
Proving a finite group of some given finite order is not simple is a standard homework problem in abstract algebra courses.
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Proving a finite group of some given finite order is not simple is a standard homework problem in abstract algebra courses.
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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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, 2010
Davenport’s Problem asks: What can we expect of two polynomials, over Z, with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport, Lewis and Schinzel.By bounding the degrees, but ...
M. Fried
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Davenport’s Problem asks: What can we expect of two polynomials, over Z, with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport, Lewis and Schinzel.By bounding the degrees, but ...
M. Fried
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