Results 41 to 50 of about 12,692,686 (297)
Some Residual Properties of Finite Rank Groups
Моделирование и анализ информационных систем, 2014 The generalization of one classical Seksenbaev theorem for polycyclic groups is obtained. Seksenbaev proved that if G is a polycyclic group which is residually finite p-group for infinitely many primes p, it is nilpotent. Recall that a group G is said to
D. N. Azarov
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Orbit-counting for nilpotent group shifts [PDF]
, 2007 We study the asymptotic behaviour of the orbit-counting function and a dynamical Mertens' theorem for the full $G$-shift for a finitely-generated torsion-free nilpotent group $G$.
R. Miles, T. Ward
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Generalized nilpotent braces and nilpotent groups
International Journal of Group Theory, 2023 A left brace is a set \((B, +, \cdot)\) equipped with two operations: \begin{enumerate} \item[(1)] \((B, +)\) forms an abelian group. \item[(2)] \((B, \cdot)\) forms a group. \item[(3)] The two operations are linked by the relation: \[ a \cdot (b + c) + a = a \cdot b + a \cdot c, \] for all \(a, b, c \in B\).
Dixon, Martyn +2 more
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Nilpotent Group C*-algebras as Compact Quantum Metric Spaces [PDF]
Canadian mathematical bulletin, 2002 Let $\mathbb{L}$ be a length function on a group $G$ , and let ${{M}_{\mathbb{L}}}$ denote the operator of pointwise multiplication by $\mathbb{L}$ on ${{\ell }^{2}}\left( G \right)$ .
M. Christ, Marc A. Rieòel
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The action of a nilpotent group on its horofunction boundary has finite orbits [PDF]
, 2008 We study the action of a nilpotent group G with finite generating set S on its horofunction boundary. We show that there is one finite orbit associated to each facet of the polytope obtained by projecting S into the infinite component of the ...
C. Walsh
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Equations in nilpotent groups [PDF]
Proceedings of the American Mathematical Society, 2015 We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commutator, which includes the higher Heisenberg groups. We also prove that the decision problem for systems of equations is unsolvable in all non-abelian free nilpotent groups.
Duchin, Moon +2 more
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Countingp-groups and nilpotent groups [PDF]
Publications mathématiques de l'IHÉS, 2000 What can one say about the function \(f(p,n)\) that counts (up to isomorphism) groups of order \(p^n\), where \(p\) is a prime, and \(n\) is an integer? \textit{G. Higman} [Proc. Lond. Math. Soc. (3) 10, 24-30 (1960; Zbl 0093.02603)] and \textit{C. C. Sims} [Proc. Lond. Math. Soc. (3) 15, 151-166 (1965; Zbl 0133.28401)] have given an asymptotic formula
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Finite p′-nilpotent groups. II
International Journal of Mathematics and Mathematical Sciences, 1987 In this paper we continue the study of finite p′-nilpotent groups that was started in the first part of this paper. Here we give a complete characterization of all finite groups that are not p′-nilpotent but all of whose proper subgroups are p′-nilpotent.
S. Srinivasan
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International Journal of Mathematics and Mathematical Sciences, 1987 In this paper we consider finite p′-nilpotent groups which is a generalization of finite p-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in ...
S. Srinivasan
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Journal of Algebra, 1995 Let \(D\) be a division ring, \(V\) a vector space over \(D\) of infinite dimension. Say that an element \(g \in \text{GL} (V)\) is cofinitary if \(\dim_D C_V (g)\) is finite. A subgroup \(G \leq \text{GL} (V)\) is called cofinitary if all its non-trivial elements are cofinitary.
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