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Nilpotent Lie Groups

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Nilpotent Groups

Springer Monographs in Mathematics, 2021
Tullio Ceccherini-Silberstein, Michele D’Adderio   +1 more
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On the proper enhanced power graphs of finite nilpotent groups

Journal of group theroy, 2022
For a group 𝐺, the enhanced power graph of 𝐺 is a graph with vertex set 𝐺 in which two distinct vertices x , y x,y are adjacent if and only if there exists an element 𝑤 in 𝐺 such that both 𝑥 and 𝑦 are powers of 𝑤.
S. Bera, Hiranya Kishore Dey
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Polynomial averages and pointwise ergodic theorems on nilpotent groups

Inventiones Mathematicae, 2021
We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on $$\sigma $$ σ -finite measure spaces.
A. Ionescu, Á. Magyar, Mariusz Mirek, T. Szarek   +3 more
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On pointed Hopf algebras over nilpotent groups

Israel Journal of Mathematics, 2021
We classify finite-dimensional Nichols algebras over finite nilpotent groups of odd order in group-theoretical terms. The main step is to show that the conjugacy classes of such finite groups are either abelian or of type C; this property also holds for ...
N. Andruskiewitsch
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NILPOTENCY IN UNCOUNTABLE GROUPS

Journal of the Australian Mathematical Society, 2016
The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}
De Giovanni, Francesco, Trombetti, Marco
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Automorphism Groups of Nilpotent Groups

Bulletin of the London Mathematical Society, 1989
Let \({\mathfrak X}\) denote the class of all finitely generated torsion-free nilpotent groups G such that the derived factor group G/G' is torsion- free. For G in \({\mathfrak X}\), let Aut *(G) denote the group of automorphisms of G/G' induced by the automorphism group of G. If G/G' has rank n and we choose a \({\mathbb{Z}}\)-basis for G/G' then Aut *
Bryant, R. M., Papistas, A.
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TC0 Circuits for Algorithmic Problems in Nilpotent Groups

International Symposium on Mathematical Foundations of Computer Science, 2017
Recently, Macdonald et. al. showed that many algorithmic problems for finitely generated nilpotent groups including computation of normal forms, the subgroup membership problem, the conjugacy problem, and computation of subgroup presentations can be done
A. Myasnikov, A. Weiss
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Membership problems in nilpotent groups

journal of Groups, complexity, cryptology
We study both the Submonoid Membership problem and the Rational Subset Membership problem in finitely generated nilpotent groups. We give two reductions with important applications.
Corentin Bodart
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Nilpotent Groups

1994
Abstract With the general theory of the previous chapter in hand, we can begin the structural analysis of groups of finite Morley rank. The general theory occupies Chapters 6 through 9. The present chapter deals with the structure theory for nilpotent groups.
Alexandre Borovik, Ali Nesin
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