Results 31 to 40 of about 46,813 (198)
The t-Fibonacci sequences in the 2-generator p-groups of nilpotency class 2 [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we consider the 2-generator p-groups of nilpotency class 2. We will discuss the lengths of the periods of the t-Fibonacci sequences in these groups.
Elahe Mehraban +2 more
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Definable Envelopes of Nilpotent Subgroups of Groups with Chain Conditions on Centralizers [PDF]
, 2011 An $\mathfrak{M}_C$ group is a group in which all chains of centralizers have finite length. In this article, we show that every nilpotent subgroup of an $\mathfrak{M}_C$ group is contained in a definable subgroup which is nilpotent of the same ...
Altınel, Tuna, Baginski, Paul
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Random Nilpotent Groups I [PDF]
International Mathematics Research Notices, 2017 We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to infinity. Whereas random groups are quotients of a free group by such a random set of relators, random nilpotent groups are formed as corresponding quotients ...
Cordes, Matthew +4 more
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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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On the primitive irreducible representations of finitely generated nilpotent groups
Доповiдi Нацiональної академiї наук України, 2021 We develop some tecniques whish allow us to apply the methods of commutative algebra for studing the representations of nilpotent groups. Using these methods, in particular, we show that any irreducible representation of a finitely generated nilpotent ...
A.V. Tushev
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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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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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