Results 41 to 50 of about 9,042,434 (209)
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
doaj +1 more source
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
openaire +2 more sources
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
doaj +1 more source
Solvable Lie A-algebras. [PDF]
, 2011 A finite-dimensional Lie algebra $L$ over a field $F$ is called an $A$-algebra if all of its nilpotent subalgebras are abelian. This is analogous to the concept of an $A$-group: a finite group with the property that all of its Sylow subgroups are abelian.
Towers, David A.
core +5 more sources
Journal of Algebra, 2006 Let \(G\) be a finite group and order the set of sizes of conjugacy classes of \(G\) decreasingly to obtain what is called the conjugate type vector of \(G\). The authors show by examples that if \(H\) is nilpotent and if \(G\) and \(H\) have the same conjugate type vector, then \(G\) is not necessarily nilpotent.
Camina, A.R., Camina, R.D.
openaire +2 more sources
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
doaj +1 more source
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
doaj +1 more source
On Torsion-by-Nilpotent Groups
Journal of Algebra, 2001 Here are the main results of the article under review: Theorem 1.1. Let \(\wp\) be a class of groups, which is closed under taking subgroups and quotients. Suppose that all metabelian groups of \(\wp\) are torsion-by-nilpotent. Then all soluble groups of \(\wp\) are torsion-by-nilpotent. Theorem 1.2. Let \(H\) be a normal subgroup of a group \(G\). If \
Endimioni, Gérard, Traustason, Gunnar
openaire +1 more source
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
openaire +5 more sources
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
doaj +1 more source