Results 31 to 40 of about 518 (187)
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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Ricci-flat and Einstein pseudoriemannian nilmanifolds
Complex Manifolds, 2019 This is partly an expository paper, where the authors’ work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group.
Conti Diego, Rossi Federico A.
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Holographic duals of 6d RG flows
Journal of High Energy Physics, 2019 A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer N , an ADE group G, and two nilpotent elements μ L,R in G. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with
G. Bruno De Luca +3 more
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Nilpotent Groups Acting on Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1993 In this paper, we study certain properties of the group ring of a nilpotent group which are related to commutativity and conjugation. We establish some relations involving conjugates of the elements of the group ring; these relations are then used to get a better understanding of torsion in abelian-by-nilpotent groups; we shall see notably that given ...
Cassidy, Charles, Laberge, Guy
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Locally Nilpotent Linear Groups
Irish Mathematical Society Bulletin, 2005 We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.
Detinko, A. S., Flannery, D. L.
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Groups with conjugacy classes of coprime sizes
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract Suppose that x$x$, y$y$ are elements of a finite group G$G$ lying in conjugacy classes of coprime sizes. We prove that ⟨xG⟩∩⟨yG⟩$\langle x^G \rangle \cap \langle y^G \rangle$ is an abelian normal subgroup of G$G$ and, as a consequence, that if x$x$ and y$y$ are π$\pi$‐regular elements for some set of primes π$\pi$, then xGyG$x^G y^G$ is a π ...
R. D. Camina +8 more
wiley +1 more source