Results 31 to 40 of about 795,041 (278)
Cyclically separated groups [PDF]
Bulletin of the Australian Mathematical Society, 1982 We call a group G cyclically separated if for any given cyclic subgroup B in G and subgroup A of finite index in B, there exists a normal subgroup N of G of finite index such that N ∩ B = A. This is equivalent to saying that for each element x ∈ G and integer n ≥ 1 dividing the order o(x) of x, there exists a normal subgroup N of G of finite index such
Hartley, Brian +2 more
openaire +2 more sources
Uniform cyclic group factorizations of finite groups
Communications in Algebra, 2023 In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there exist subgroups $H_1, H_2, \ldots, H_k$ such that $G = H_1 H_2 \cdots H_k$ and the number of ways to represent any ...
Kazuki Kanai +3 more
openaire +2 more sources
The quaternion-type cyclic-balancing sequence in groups [PDF]
Notes on Number Theory and Discrete MathematicsIn this research, several types of definitions of the quaternion-type cyclic-balancing sequence are presented. The Cassini formula and generating function of these sequences are also obtained for all types.
Nazmiye Yılmaz +2 more
doaj +1 more source
Polish Topologies for Graph Products of Cyclic Groups [PDF]
, 2018 We give a complete characterization of the graph products of cyclic groups admitting a Polish group topology, and show that they are all realizable as the group of automorphisms of a countable structure.
Paolini, Gianluca, Shelah, Saharon
core +2 more sources
On logically cyclic groups [PDF]
Journal of Group Theory, 2014 Abstract A group G is called logically cyclic if it has an element s such that every element of G can be defined by a first-order formula with parameter s. The aim of this paper is to investigate the structure of such groups.
openaire +2 more sources
Crosscap of the non-cyclic graph of groups
AKCE International Journal of Graphs and Combinatorics, 2016 The non-cyclic graph CG to a non locally cyclic group G is as follows: take G∖Cyc(G) as vertex set, where Cyc(G)={x∈G|〈x,y〉 is cyclic for all y∈G} is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup.
K. Selvakumar, M. Subajini
doaj +1 more source
Torsion locally nilpotent groups with non-Dedekind norm of Abelian non-cyclic subgroups
Karpatsʹkì Matematičnì Publìkacìï, 2022 The authors study relations between the properties of torsion locally nilpotent groups and their norms of Abelian non-cyclic subgroups. The impact of the norm of Abelian non-cyclic subgroups on the properties of the group under the condition of norm non ...
T.D. Lukashova, M.G. Drushlyak
doaj +1 more source
LOG Groups and Cyclically Presented Groups
Journal of Algebra, 1995 A labelled oriented graph (LOG) is a directed graph together with a labelling of its edges by vertices. It determines a group presentation with generators corresponding to the vertices, and relators determined by the edges where the relator says that the edge label conjugates the (generator corresponding to the) initial vertex of the edge to the ...
Gilbert, N.D., Howie, J.
openaire +2 more sources
Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$
Discrete Analysis, 2019 Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$, Discrete Analysis 2019:14, 14 pp. A conjecture of Fuglede from 1974 states that a measurable set $E\subset \mathbb R^n$ of positive Lebesgue measure has a set of translates that tile ...
Ruxi Shi
doaj +1 more source
, 2021 CYCLIC GROUP and its underlying definitions are presented in this white paper (knowledge base).
openaire +1 more source