Generic -coverings of finite groups of Lie type
Les « groupes totaux » sont les groupes pour lesquels la dimension du centre l’algèbre des invariants d’une algèbre simple centrale associée à un -cocycle sous l’action d’un relevé de l’action galoisienne à est constante quels que soient et . 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...
Scriviamo ed . Cerchiamo gruppi con generatori tali che ed per alcuni numeri naturali , .
The prime graph of a finite group is defined as follows: the set of vertices is , the set of primes dividing the order of , and two vertices , are joined by an edge (we write ) if and only if there exists an element in of order . We study the groups such that the prime graph is a tree, proving that, in this case, .
Let be a finite group and write for the degree set of the complex irreducible characters of . The group is said to satisfy the two-prime hypothesis if for any distinct degrees , the total number of (not necessarily different) primes of the greatest common divisor is at most . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL for .
A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.