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Groupes totaux

Bruno Deschamps, Ivan Suarez Atias (2013)

Annales mathématiques Blaise Pascal

Les « groupes totaux » sont les groupes pour lesquels la dimension du centre l’algèbre des invariants d’une algèbre simple centrale 𝔄 f associée à un 2 -cocycle f Z 2 ( Gal ( L / k ) , L * ) sous l’action d’un relevé de l’action galoisienne à 𝔄 f est constante quels que soient k et f . Dans cet article, nous montrons que les groupes quasi-CC (qui sont les groupes de centre cyclique et dont les centralisateurs des éléments hors du centre sont cycliques) sont totaux. Les groupes de type CC qui sont les groupes quasi-CC à centre trivial...

Groups generated by two mutually Engel periodic elements

H. Heineken (2000)

Bollettino dell'Unione Matematica Italiana

Scriviamo [ x , y ] = [ x , 1 y ] ed [ [ x , k y ] , y ] = [ x , k + 1 y ] . Cerchiamo gruppi S L 2 , q con generatori x , y tali che [ x , m y ] = x ed [ y , n x ] = y per alcuni numeri naturali m , n .

Groups in which the prime graph is a tree

Maria Silvia Lucido (2002)

Bollettino dell'Unione Matematica Italiana

The prime graph Γ G of a finite group G is defined as follows: the set of vertices is π G , the set of primes dividing the order of G , and two vertices p , q are joined by an edge (we write p q ) if and only if there exists an element in G of order p q . We study the groups G such that the prime graph Γ G is a tree, proving that, in this case, π G 8 .

Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL 2 ( q ) for q 7

Mark L. Lewis, Yanjun Liu, Hung P. Tong-Viet (2018)

Czechoslovak Mathematical Journal

Let G be a finite group and write cd ( G ) for the degree set of the complex irreducible characters of G . The group G is said to satisfy the two-prime hypothesis if for any distinct degrees a , b cd ( G ) , the total number of (not necessarily different) primes of the greatest common divisor gcd ( a , b ) is at most 2 . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL 2 ( q ) for q 7 .

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

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