Results 221 to 230 of about 1,361,110 (264)

Index Four Simple Groups

Canadian Journal of Mathematics, 1978
An index four simple group is a finite simple group, G, with a self-centralizing Sylow p-subgroup whose normalizer in G has order 4p. In this paper index four simple groups having a non-principal ordinary irreducible character of small degree in the ...
Alex, Leo J., Morrow, Dean C.
openaire   +2 more sources

Shunkov Groups Saturated with Almost Simple Groups

Algebra and Logic, 2023
A group \(G\) is a Shunkov group if whenever \(H\) is a finite subgroup of \(G\) any two conjugate elements of prime order in the group \(N_G(H)/H\) generate a finite subgroup. The class of such groups forms a generalization of the class of locally finite groups.
Maslova, N. V., Shlepkin, A. A.
openaire   +1 more source

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
openaire   +2 more sources

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 ...
openaire   +1 more source

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 ...
openaire   +2 more sources

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.
openaire   +2 more sources

Groups saturated by finite simple groups

Algebra and Logic, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

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
openaire   +1 more source

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
openaire   +1 more source

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 ...
openaire   +1 more source