Search results for "Omega-saturated formation"

showing 2 items of 2 documents

On X-saturated formations of finite groups

2005

[EN] In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques are also very useful to highlight the properties and behaviour of omega-local formations. In fact, extensions and improvements of several results of Shemetkov are natural consequences of our study.

Class (set theory)Finite groupAlgebra and Number TheorySaturated formationGrups Teoria deP-saturated formationX-local formationLocal formationOmega-local formationGeneralized frattini subgroupOmega-saturated formationAlgebraSimple groupX-saturated formationÀlgebraFinite groupAlgebra over a fieldMATEMATICA APLICADAMathematics
researchProduct

A question from the Kourovka Notebook on formation products

2003

[EN] It is shown in this paper that if X is a class of simple groups such that pi(X) = char X, the X-saturated formation H generated by a finite group cannot be expressed as the Gaschütz product F o G of two non-X-saturated formations if H = G. It answers some open questions on products of formations. The relation between omega-saturated and X-saturated formations is also discussed.

Finite groupPure mathematicsClass (set theory)Relation (database)Saturated formationComposition formationGeneral MathematicsX-local formationMatemàtica aplicadaOmega-saturated formationSimple groupProduct (mathematics)X-saturated formationFinite groupMATEMATICA APLICADAMathematics
researchProduct