Search results for "subnormal subgroups"

showing 2 items of 2 documents

On Formations of Finite Groups with the Wielandt Property for Residuals

2001

Abstract Given two subgroups U, V of a finite group which are subnormal subgroups of their join 〈U, V〉 and a formation F , in general it is not true that 〈U, V〉 F  = 〈U F , V F 〉. A formation is said to have the Wielandt property if this equality holds universally. A formation with the Wielandt property must be a Fitting class. Wielandt proved that the most usual Fitting formations (e.g., nilpotent groups and π-groups) have the Wielandt property. At present, neither a general satisfactory result on the universal validity of the Wielandt property nor a counterexample is known. In this paper a criterion for a Fitting formation to have the Wielandt property is given. As an application, it is p…

Discrete mathematicsClass (set theory)Pure mathematicsFinite groupProperty (philosophy)Algebra and Number Theorylattice propertiesJoin (topology)subnormal subgroupsresidualsNilpotentLattice propertiesformationsUniversal validityMathematicsCounterexampleJournal of Algebra
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On finite groups generated by strongly cosubnormal subgroups

2003

[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and sufficient conditions for A and B to be strongly cosubnormal in and, if Z is the hypercentre of G=, we show that A and B are strongly cosubnormal if and only if G/Z is the direct product of AZ/Z and BZ/Z. We also show that projectors and residuals for certain formations can easily be constructed in such a group. Two subgroups A and B of a group G are N-connected if every cyclic subgroup of A is cosubnormal with every cyclic subgroup of B (N denotes the class of nilpotent groups). Thou…

Normal subgroupFinite groupHypercentreAlgebra and Number TheoryStrongly cosubnormal subgroupsFormationN-connected subgroupsFitting subgroupCombinatoricsSubnormal subgroupSubgroupLocally finite groupCharacteristic subgroupIndex of a subgroupFinite groupMATEMATICA APLICADAMatemàticaSubnormal subgroupMathematicsNilpotent group
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