102,752 research outputs found
Preface: 18th Cologne–Twente Workshop on graphs and combinatorial optimization (CTW 2020)
No full textNonvanishing elements for Brauer characters
No full textLet G be a finite group and p a prime. We say that a p-regular element g of G is p-nonvanishing if no irreducible p-Brauer character of G takes the value 0 on g. The main result of this paper shows that if G is solvable and g is a p-regular element which is p-nonvanishing, then g lies in a normal subgroup of G whose p-length and p'-length are both at most 2 (with possible exceptions for p\leq 7), the bound being best possible. This result is obtained through the analysis of one particular orbit condition in linear actions of solvable groups on finite vector spaces, and it generalizes (for p>7) some results in Dolfi and Pacifici [‘Zeros of Brauer characters and linear actions of finite groups’, J. Algebra 340 (2011), 104–113]
Exact Algorithms for a discrete metric labeling problem
No full textAbstractWe are given a edge-weighted undirected graph G=(V,E) and a set of labels/colors C={1,2,…,p}. A non-empty subset Cv⊆C is associated with each vertex v∈V. A coloring of the vertices is feasible if each vertex v is colored with a color of Cv. A coloring uniquely defines a subset E′⊆E of edges having different colored endpoints. The problem of finding a feasible coloring which defines a minimum weight E′ is, in general, NP-hard. In this work we first propose polynomial time algorithms for some special cases, namely when the input graph is a tree, a cactus or with bounded tree-width. Then, an implicit enumeration scheme for finding an optimal coloring in the general case is described and computational results are presented
On tensor factorisation for representations of finite groups
No full textWe prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G
On the number of anisotropic simple submodules in modules with a form
No full textLet G be a finite group, and V a finite-dimensional semisimple G-module over a finite field. Assume that V is endowed with a nonsingular bilinear form which is symmetric or symplectic, and which is invariant under the action of G. In this setting, we compute the number of anisotropic simple submodules of V
Minimizing Part Transfer Costs in Flexible Manufacturing Systems: A Computational Study on Different Lower Bounds
No full text
On tensor induction for representations of finite groups
No full textAbstractIt is well known that if D is an irreducible complex representation of a finite group G, then every direct summand of the restriction of D to a subgroup H must have degree at least as large as the degree of D divided by the index |G:H|; moreover, D is induced from H if and only if the restriction does have a direct summand whose dimension is equal to this quotient. This paper explores the possibility of an analogous result for tensor induction, under the additional assumption that D is faithful, quasi-primitive and not a tensor product (of projective representations of degree greater than 1), and that the Fitting subgroup F(G) is not in the centre Z(G). The main question is this: if the restriction has a (projective) tensor factor whose degree is the |G:H|th root of the degree of D, does it follow that D is tensor induced from H? Among other results, examples are given to show that the answer can be negative when the index is 2. An affirmative answer is proved for normal subgroups of odd index, and also for arbitrary subgroups of odd prime index. As might be expected, the key lies in the study of F(G)/Z(G) as a symplectic module over a finite prime field; in particular, in exploring the connection between (ordinary) induction and form-induction of such modules
On the structure of induced modules and tensor induction for group representations
No full textLet V be a simple module for a finite group G, over a finite field F, and let H be a subgroup of G. Assuming that V is induced by an FH-module, we investigate some aspects of the structure of V viewed as a module for H. This kind of analysis turns out to play a central role in a problem concerning tensor induction for representations of finite groups
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