scholarly journals On Forbidden Poset Problems in the Linear Lattice

10.37236/8831 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Jimeng Xiao ◽  
Casey Tompkins
Keyword(s):  
Vector Space ◽  
Large Range ◽  
Maximum Size ◽  
Linear Lattice ◽  
Finite Vector ◽  
Finite Vector Space ◽  
Forbidden Poset ◽  
Vector Subspaces

In this note, we determine the maximum size of a $\{\mathrm{V}_{k}, \Lambda_{l}\}$-free family in the lattice of vector subspaces of a finite vector space both in the non-induced case as well as the induced case, for a large range of parameters $k$ and $l$. These results generalize earlier work by Shahriari and Yu.  We also prove a general LYM-type lemma for the linear lattice which resolves a conjecture of Shahriari and Yu.  

The maximum size of a partial 3-spread in a finite vector space over GF(2)

2009 ◽  
Vol 54 (2) ◽  
pp. 101-107 ◽  
Author(s):  
S. El-Zanati ◽  
H. Jordon ◽  
G. Seelinger ◽  
P. Sissokho ◽  
L. Spence
Keyword(s):  
Vector Space ◽  
Maximum Size ◽  
Finite Vector ◽  
Finite Vector Space

Orbits and Stabilizers for Solvable Linear Groups

2006 ◽  
Vol 49 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Jeffrey M. Riedl
Keyword(s):  
Vector Space ◽  
Finite Groups ◽  
Irreducible Character ◽  
General Class ◽  
Frobenius Group ◽  
Solvable Groups ◽  
Character Degrees ◽  
Linear Groups ◽  
Finite Vector ◽  
Finite Vector Space

AbstractWe extend a result of Noritzsch, which describes the orbit sizes in the action of a Frobenius group G on a finite vector space V under certain conditions, to a more general class of finite solvable groups G. This result has applications in computing irreducible character degrees of finite groups. Another application, proved here, is a result concerning the structure of certain groups with few complex irreducible character degrees.

scholarly journals On the orders of primitive linear P'-groups

1993 ◽  
Vol 48 (3) ◽  
pp. 495-521 ◽  
Author(s):  
A. Gambini Weigel ◽  
T.S. Weigel
Keyword(s):  
Vector Space ◽  
Lower Bounds ◽  
Minimal Representation ◽  
Group Order ◽  
Finite Vector ◽  
Finite Vector Space

A group G ≤ GLK(V) is called K-primitive if there exists no non-trivial decomposition of V into a sum of K-spaces which is stabilised by G. We show that if V is a finite vector space and G a K-primitive subgroup of GLK(V) whose order is coprime to |V|, we can bound the order of G by |V|log2(|V|) apart from one exception. Later we use this result to obtain some lower bounds on the number of p–singular elements in terms of the group order and the minimal representation degree.

scholarly journals Automorphism groups of some variants of lattices

2021 ◽  
Vol 13 (1) ◽  
pp. 142-148
Author(s):  
O.G. Ganyushkin ◽  
O.O. Desiateryk
Keyword(s):  
Automorphism Group ◽  
Vector Space ◽  
Wreath Product ◽  
Automorphism Groups ◽  
Symmetric Groups ◽  
Natural Generalization ◽  
Space Lattice ◽  
Finite Vector ◽  
Finite Vector Space ◽  
Finite Set

In this paper we consider variants of the power set and the lattice of subspaces and study automorphism groups of these variants. We obtain irreducible generating sets for variants of subsets of a finite set lattice and subspaces of a finite vector space lattice. We prove that automorphism group of the variant of subsets of a finite set lattice is a wreath product of two symmetric permutation groups such as first of this groups acts on subsets. The automorphism group of the variant of the subspace of a finite vector space lattice is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the automorphism group of subspaces lattice and the second is defined by the certain set of symmetric groups.

scholarly journals On resolvability of a graph associated to a finite vector space

2019 ◽  
Vol 18 (02) ◽  
pp. 1950029
Author(s):  
U. Ali ◽  
S. A. Bokhary ◽  
K. Wahid ◽  
G. Abbas
Keyword(s):  
Vector Space ◽  
Domination Number ◽  
Exchange Property ◽  
Metric Dimension ◽  
Resolving Set ◽  
Matroid Intersection ◽  
Finite Vector ◽  
Finite Vector Space ◽  
Partition Dimension ◽  
Matroid Intersection Problem

In this paper, the resolving parameters such as metric dimension and partition dimension for the nonzero component graph, associated to a finite vector space, are discussed. The exact values of these parameters are determined. It is derived that the notions of metric dimension and locating-domination number coincide in the graph. Independent sets, introduced by Boutin [Determining sets, resolving set, and the exchange property, Graphs Combin. 25 (2009) 789–806], are studied in the graph. It is shown that the exchange property holds in the graph for minimal resolving sets with some exceptions. Consequently, a minimal resolving set of the graph is a basis for a matroid with the set [Formula: see text] of nonzero vectors of the vector space as the ground set. The matroid intersection problem for two matroids with [Formula: see text] as the ground set is also solved.

scholarly journals Counting subspaces of a finite vector space — 2

Resonance ◽  
2010 ◽  
Vol 15 (12) ◽  
pp. 1074-1083 ◽  
Author(s):  
Amritanshu Prasad
Keyword(s):  
Vector Space ◽  
Finite Vector ◽  
Finite Vector Space

scholarly journals The affinity of a permutation of a finite vector space

2007 ◽  
Vol 13 (1) ◽  
pp. 80-112
Author(s):  
W. Edwin Clark ◽  
Xiang-dong Hou ◽  
Alec Mihailovs
Keyword(s):  
Vector Space ◽  
Finite Vector ◽  
Finite Vector Space

scholarly journals Orthogonality and complementation in the lattice of subspaces of a finite vector space

2021 ◽  
pp. 1-13
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Vector Space ◽  
Finite Vector ◽  
Finite Vector Space

scholarly journals Covering codes of a graph associated to a finite vector space

2020 ◽  
Vol 72 (7) ◽  
pp. 952-959
Author(s):  
M. Murtaza ◽  
I. Javaid ◽  
M. Fazil
Keyword(s):  
Vector Space ◽  
Domination Number ◽  
Exchange Property ◽  
Dominating Sets ◽  
Identifying Codes ◽  
Finite Vector ◽  
Finite Vector Space ◽  
Covering Codes

UDC 512.5 In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das [Commun. Algebra, <strong>44</strong>, 3918 – 3926 (2016)], such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-dominating sets and identifying codes, which are closely related concepts for this purpose. We find the location-domination number and the identifying number of the graph and study the exchange property for locating-dominating sets and identifying codes.

scholarly journals On sets of vectors of a finite vector space in which every subset of basis size is a basis II

2012 ◽  
Vol 65 (1-2) ◽  
pp. 5-14 ◽  
Author(s):  
Simeon Ball ◽  
Jan De Beule
Keyword(s):  
Vector Space ◽  
Finite Vector ◽  
Finite Vector Space ◽  
Basis Size
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