Results 11 to 20 of about 12,692,686 (297)

DISTORTION IN FREE NILPOTENT GROUPS [PDF]

International Journal of Algebra and Computation, 2010
We prove that a subgroup of a finitely generated free nilpotent group F is undistorted if and only if it is a retract of a subgroup of finite index in F.
Tara C. Davis
openaire   +5 more sources

Omegas of agemos in powerful groups [PDF]

International Journal of Group Theory, 2020
In this note we show that for any powerful $p$-group $G$‎, ‎the subgroup‎ ‎$\Omega_{i}(G^{p^{j}})$ is powerfully nilpotent for all $i,j\geq1$‎ ‎when $p$ is an odd prime‎, ‎and $i\geq1$‎, ‎$j\geq2$ when $p=2$‎.
James Williams
doaj   +1 more source

On Some Residual Properties of the Verbal Embeddings of Groups [PDF]

Advances in Group Theory and Applications, 2016
We consider verbal embedding constructions preserving some residual properties for groups. An arbitrary residually finite countable group $H$ has a $V$-verbal embedding into a residually finite $2$-generator group $G$ for any non-trivial word set $V$. If
Vahagn H. Mikaelian
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Nilpotent groups are round [PDF]

Israel Journal of Mathematics, 2008
We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of the group. Our main result is that this combinatorial property is equivalent to nilpotence.
Berend, Daniel, Boshernitzan, Michael D.
openaire   +3 more sources

A nilpotent group without local functional equations for pro-isomorphic subgroups [PDF]

, 2014
The pro-isomorphic zeta function ζΓ∧(s) of a torsion-free finitely generated nilpotent group Γ enumerates finite index subgroups Δ ≤ Γ such that Δ and Γ have isomorphic profinite completions.
Mark N. Berman, B. Klopsch
semanticscholar   +1 more source

Finitely generated nilpotent group C*-algebras have finite nuclear dimension [PDF]

, 2014
We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra $A$ generated by an irreducible representation of such a group has decomposition ...
C. Eckhardt, P. McKenney
semanticscholar   +1 more source

On Malle’s conjecture for nilpotent groups

Transactions of the American Mathematical Society. Series B, 2023
We develop an abstract framework for studying the strong form of Malle’s conjecture [J. Number Theory 92 (2002), pp. 315–329; Experiment. Math. 13 (2004), pp. 129–135] for nilpotent groups G G in their regular representation.
P. Koymans, Carlo Pagano
semanticscholar   +1 more source

Endomorphism kernel property for finite groups [PDF]

Mathematica Bohemica, 2022
A group $G$ has the endomorphism kernel property (EKP) if every congruence relation $\theta$ on $G$ is the kernel of an endomorphism on $G$. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian ...
Heghine Ghumashyan, Jaroslav Guričan
doaj   +1 more source

Strongly Ad-Nilpotent Elements of the Lie Algebra of Upper Triangular Matrices

Journal of Mathematics, 2022
In this paper, the strongly ad-nilpotent elements of the Lie algebra tn,ℂ of upper triangular complex matrices are studied. We prove that all the nilpotent matrices in tn,ℂ are strongly ad-nilpotent if and only if n≤6. Additionally, we prove that all the
Zhiguang Hu
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Groups whose Proper Subgroups of Infinite Rank are Minimax-by-Nilpotent or Nilpotent-by-Minimax [PDF]

Advances in Group Theory and Applications, 2020
Let M denote the class of of soluble-by-finite minimax groups, and N the class of nilpotent groups. The main result states that if G is a group of infinite rank whose proper subgroups of infinite rank are MN-groups, then G is either in MN or it is a ...
Amel Zitouni
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