Results 291 to 300 of about 5,163,657 (332)

Generators for Simple Groups

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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SIMPLE ALMOST HYPERDEFINABLE GROUPS

Journal of Mathematical Logic, 2006
(i) We lay down the groundwork for the treatment of almost hyperdefinable groups: notions from [5] are put into a natural hierarchy, and new notions, essential to the study to such groups, fit elegantly into this hierarchy. (ii) We show that "classical" properties of definable and hyperdefinable groups in simple theories can be generalised to this ...
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A characteristically simple group

Mathematical Proceedings of the Cambridge Philosophical Society, 1954
The 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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On Simple Pseudofinite Groups

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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Groups saturated by finite simple groups

Algebra and Logic, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finite Simple Groups

The American Mathematical Monthly, 1977
(1977). Finite Simple Groups. The American Mathematical Monthly: Vol. 84, No. 9, pp. 693-714.
James F. Hurley, Arunas Rudvalis
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Boolean simple groups and boolean simple rings

The Journal of Symbolic Logic, 1988
Let 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
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Locally Finite Simple Groups

1974
The group G is locally finite if each of its finitely generated subgroups is finite. Until rather recently the area of locally finite groups entirely belonged to the wilderness of counter-examples; and there absurdly wild behaviour is possible, indeed. What little progress has been made in cultivating some fringes of this wilderness is essentially due ...
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Finite Permutation Groups and Finite Simple Groups

Bulletin of the London Mathematical Society, 1981
In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced.
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Finite Simple Groups

2003
In a statistical sense, the simple groups (by which we mean, in this window, non-abelian finite simple groups) are quite rare: the Godfather of the subject has likened them to fossils, occasionally found buried among the composition factors of a general finite group [Thompson 1984].
Alexander Lubotzky, Dan Segal
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