Search results for "Torsion subgroup"

showing 3 items of 3 documents

Hyper-abelian groups with finite co-central rank

2004

AbstractA group G has finite co-central rank s if there exists a least non-negative integer s such that every finitely generated subgroup H can be generated by at most s elements modulo the centre of H. The investigation of such groups has been started in [J.P. Sysak, A. Tresch, J. Group Theory 4 (2001) 325]. It is proved that hyper-abelian groups with finite co-central rank are locally soluble. The interplay between the Prüfer rank condition, the condition of having finite abelian section rank and the finite co-central rank condition is studied. As one result, a hyper-abelian group G with finite co-central rank has an ascending series with abelian factors of finite rank and every chief fac…

CombinatoricsAlgebra and Number TheoryTorsion subgroupRank conditionLocally finite groupPrüfer rankElementary abelian groupCyclic groupAbelian groupRank of an abelian groupMathematicsJournal of Algebra
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Abelian gradings on upper-triangular matrices

2003

Let G be an arbitrary finite abelian group. We describe all possible G-gradings on an upper-triangular matrix algebra over an algebraically closed field of characteristic zero.

CombinatoricsTorsion subgroupG-moduleGeneral MathematicsElementary abelian groupAbelian categoryAbelian groupRank of an abelian groupFree abelian groupArithmetic of abelian varietiesMathematicsArchiv der Mathematik
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A characteristic subgroup and kernels of Brauer characters

2005

If G is finite group and P is a Sylow p-subgroup of G, we prove that there is a unique largest normal subgroup L of G such that L ⋂ P = L ⋂ NG (P). If G is p-solvable, then L is the intersection of the kernels of the irreducible Brauer characters of G of degree not divisible by p.

Normal subgroupCombinatoricsMaximal subgroupTorsion subgroupBrauer's theorem on induced charactersGeneral MathematicsSylow theoremsCommutator subgroupCharacteristic subgroupFitting subgroupMathematicsBulletin of the Australian Mathematical Society
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