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RESEARCH PRODUCT
On finite groups generated by strongly cosubnormal subgroups
John CosseyAdolfo Ballester-bolinchesRamon Esteban-romerosubject
Normal subgroupFinite groupHypercentreAlgebra and Number TheoryStrongly cosubnormal subgroupsFormationN-connected subgroupsFitting subgroupCombinatoricsSubnormal subgroupSubgroupLocally finite groupCharacteristic subgroupIndex of a subgroupFinite groupMATEMATICA APLICADAMatemàticaSubnormal subgroupMathematicsNilpotent groupdescription
[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). Though the concepts of strong cosubnormality and N-connectedness are clearly closely related, we give an example to show that they are not equivalent. We note, however, that if G is the product of the N-connected subgroups A and B, then A and B are strongly cosubnormal.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-01-01 |