Results 221 to 230 of about 1,692,668 (268)
Some of the next articles are maybe not open access.
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
openaire +3 more sources
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
openaire +3 more sources
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
openaire +2 more sources
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
openaire +2 more sources
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.
openaire +1 more source
Proving a finite group of some given finite order is not simple is a standard homework problem in abstract algebra courses.
openaire +1 more source
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
openaire +2 more sources
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
openaire +2 more sources
On the Spread of Finite Simple Groups
Combinatorica, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robert M. Guralnick, Aner Shalev
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire +2 more sources
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 ...
openaire +2 more sources
Boolean simple groups and boolean simple rings
The Journal of Symbolic Logic, 1988Let be a complete Boolean algebra and G a finite simple group in the Scott-Solovay -valued model V() of set theory. If we observe G outside V(), then we get a new group which is denoted by Ĝ. In general, Ĝ is not finite nor simple. Nevertheless Ĝ satisfies every property satisfied by a finite simple group with some translation. In this way, we can get
openaire +1 more source
Groups saturated by finite simple groups
Algebra and Logic, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
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 ...
openaire +1 more source