Results 31 to 40 of about 301 (136)
Pseudocomplete nilpotent groups [PDF]
Proceedings of the American Mathematical Society, 1983 Semicomplete nilpotent groups, that is, nilpotent groups with no outer automorphisms, have been of interest for many years. In this paper pseudocomplete nilpotent groups, that is, nilpotent groups in which the automorphism group and the inner automorphism group are isomorphic (not equal), are constructed.
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Glasgow Mathematical Journal, 2019 AbstarctLetγn= [x1,…,xn] be thenth lower central word. Denote byXnthe set ofγn-values in a groupGand suppose that there is a numbermsuch that$|{g^{{X_n}}}| \le m$for eachg∈G. We prove thatγn+1(G)has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.
ELOISA DETOMI +3 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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On Finite Nilpotent Groups [PDF]
Canadian Journal of Mathematics, 1960 It is well known that if (n, ϕ(n)) = 1, where ϕ(n) denotes the Euler ϕ function, then the only group of order n is the cyclic group. This is a special case of a more general result due to Dickson (2, p. 201); namely, ifwhere the pi are distinct primes and each αi > 0, the necessary and sufficient conditions that the only groups of order n are ...
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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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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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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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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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Computing in Nilpotent Matrix Groups [PDF]
LMS Journal of Computation and Mathematics, 2006 AbstractWe present algorithms for testing nilpotency of matrix groups over finite fields, and for deciding irreducibility and primitivity of nilpotent matrix groups. The algorithms also construct modules and imprimitivity systems for nilpotent groups.
A. S. Detinko, Dane L. Flannery
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