Search results for "Nilpotent group"

showing 7 items of 47 documents

On finite minimal non-nilpotent groups

2005

[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol¿fand¿s theorem on maximal Schmidt groups.

Pure mathematicsFinite groupPst-groupMathematical societyApplied MathematicsGeneral MathematicsGrups Teoria deSchmidt groupSylow subgroupSylow-permutable subgroupAlgebraMinimal non-nilpotent groupNilpotentCritical groupÀlgebraAlgebra over a fieldFinite groupClass of finite groupsMATEMATICA APLICADACritical groupVolume (compression)Mathematics
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On finite products of nilpotent groups

1994

Pure mathematicsNilpotentGeneral MathematicsNilpotent groupUnipotentCentral seriesMathematicsArchiv der Mathematik
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An uncountable family of almost nilpotent varieties of polynomial growth

2017

A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of 1) a countable family of almost nilpotent varieties of at most linear growth and 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.

Pure mathematicsSecondarySubvarietyUnipotentCentral series01 natural sciencesMathematics::Group TheoryLie algebraFOS: Mathematics0101 mathematicsMathematics::Representation TheoryMathematicsDiscrete mathematicsAlgebra and Number Theory010102 general mathematicsMathematics::Rings and AlgebrasMathematics - Rings and AlgebrasPrimary; Secondary; Algebra and Number Theory010101 applied mathematicsNilpotentSettore MAT/02 - AlgebraRings and Algebras (math.RA)Uncountable setVariety (universal algebra)Nilpotent groupPrimary
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A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

2017

AbstractCarnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.

Pure mathematicsmetric groupssub-finsler geometryengineering.material01 natural sciencesdifferentiaaligeometriasymbols.namesakesub-Finsler geometryMathematics::Metric Geometry0101 mathematics22f3014m17MathematicsPrimer (paint)QA299.6-433homogeneous groupshomogeneous spacesApplied Mathematics010102 general mathematics05 social sciencesryhmäteorianilpotent groupsCarnot groups; homogeneous groups; homogeneous spaces; metric groups; nilpotent groups; sub-Finsler geometry; sub-Riemannian geometry; Analysis; Geometry and Topology; Applied Mathematicssub-riemannian geometrysub-Riemannian geometry43a8053c17Carnot groupscarnot groupsengineeringsymbols22e25Geometry and Topology0509 other social sciences050904 information & library sciencesCarnot cycleAnalysisAnalysis and Geometry in Metric Spaces
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On Associative Rings with Locally Nilpotent Adjoint Semigroup

2003

Abstract The set of all elements of an associative ring R, not necessarily with a unit element, forms a semigroup R ad under the circle operation r ∘ s = r + s + rs for all r, s in R. This semigroup is locally nilpotent if every finitely generated subsemigroup of R ad is nilpotent (in sense of A. I. Mal'cev or B. H. Neumann and T. Taylor). The ring R is locally Lie-nilpotent if every finitely generated subring of R is Lie-nilpotent. It is proved that R ad is a locally nilpotent semigroup if and only if R is a locally Lie-nilpotent ring.

Reduced ringDiscrete mathematicsPure mathematicsAlgebra and Number TheoryMathematics::Rings and AlgebrasLocally nilpotentUnipotentSubringMathematics::Group TheoryNilpotentBicyclic semigroupNilpotent groupMathematics::Representation TheoryUnit (ring theory)MathematicsCommunications in Algebra
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Nilpotent and perfect groups with the same set of character degrees

2014

We find a pair of finite groups, one nilpotent and the other perfect, with the same set of character degrees.

Set (abstract data type)Discrete mathematicsNilpotentPure mathematicsAlgebra and Number TheoryCharacter (mathematics)Applied MathematicsNilpotent groupUnipotentCentral seriesMathematicsJournal of Algebra and Its Applications
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The Fitting Subgroup and Some Injectors of Radical Locally Finite Groups with min-pfor Allp

2003

Abstract This work was intended as an attempt to continue the study of the class ℬ of generalised nilpotent groups started in a previous paper. We present some results concerning the Fitting subgroup and the ℬ-injectors of a radical locally finite group satisfying min-p for all p.

p-groupDiscrete mathematicsPure mathematicsNilpotentAlgebra and Number TheoryLocally finite groupExtra special groupCA-groupNilpotent groupCentral seriesFitting subgroupMathematicsCommunications in Algebra
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