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401
Description of the first disc Δ1(t) of the commuting graph C(G, X) for elements of order three in symmetric groups
Published 2016“…The commuting graph C(G, X), where G is a finite group and X is a subset of G, is the graph whose vertex set is X and two distinct elements of X being joined by an edge whenever they commute in the group G. …”
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Conference or Workshop Item -
402
Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
Published 2022-08-01“…Abstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G, we consider a family of tensor network representations of its ground state subspace. …”
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403
Applications of conjunctive complex fuzzy subgroups to Sylow theory
Published 2024-01-01“…Additionally, the paper formulates the conjunctive complex fuzzy version of the Cauchy theorem for finite groups. Lastly, it defines the concept of the conjunctive complex fuzzy Sylow p-subgroup for a finite group and conducts a generalization of Sylow's theorems within a conjunctive complex fuzzy environment.…”
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404
Topological Indices of the Relative Coprime Graph of the Dihedral Group
Published 2023-07-01“…Assuming that G is a finite group and H is a subgroup of G, the graph known as the relative coprime graph of G with respect to H (denoted as Γ_(G,H)) has vertices corresponding to elements of G. …”
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405
Fermionization of fusion category symmetries in 1+1 dimensions
Published 2023-10-01“…As concrete examples, we compute the fermionization of finite group symmetries, the symmetries of finite gauge theories, and duality symmetries. …”
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406
Semisimple and G-Equivariant Simple Algebras Over Operads
Published 2017“…Let G be a finite group. There is a standard theorem on the classification of G-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of G). …”
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407
Generalized involution models for wreath products
Published 2017“…We prove that if a finite group H has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product H ≀ S[subscript n] also has a generalized involution model. …”
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408
Finite Dimensional Hopf Actions on Central Division Algebras
Published 2018“…Z(D). We show that a finite group G faithfully grades D if and only if G contains a normal abelian subgroup of index dividing d. …”
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409
Finite symmetric tensor categories with the Chevalley property in characteristic 2
Published 2021“…Equivalently, we prove that there exists a unique finite group scheme [Formula: see text] in [Formula: see text] such that [Formula: see text] is symmetric tensor equivalent to [Formula: see text]. …”
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410
Prospects for Quantum Equivariant Neural Networks
Published 2023“…We present efficient quantum algorithms for performing linear finite-group convolutions and cross-correlations on data stored as quantum states. …”
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411
Representation Theory in Complex Rank, I
Published 2015“…Knop to the case of wreath products of S[subscript n] with a finite group. Generalizing these results, we propose a method of interpolating representation categories of various algebras containing S [subscript n] (such as degenerate affine Hecke algebras, symplectic reflection algebras, rational Cherednik algebras, etc.) to complex values of n. …”
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412
A survey on elliptic curve cryptography
Published 2014“…With curve dened over a finite field, this set of points acted by an addition operation forms a finite group structure. Also known as torsion points, they are used to represent the coded messages. …”
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413
Cyclic intersection graph of subgroups of dihedral groups and its properties.
Published 2023“…In an intersection graph, each vertex conforms to a set wherein two vertices are connected by an edge if and only if their corresponding sets have a non-empty intersection. For a finite group G, a graph of its subgroups can be represented by the vertices that correspond to the subgroups of G. …”
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414
Multiplicative degree of some dihedral groups
Published 2016“…The commutativity degree of a finite group G is defined as the probability that a pair of elements x and y, chosen randomly from a group G, commute. …”
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415
Graph coloring using commuting order product prime graph
Published 2020“…Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we introduce a new graph of groups, which is a commuting order product prime graph of finite groups as a graph having the elements of G as its vertices and two vertices are adjacent if and only if they commute and the product of their order is a prime power. …”
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416
The application of GAP software in constructing the non-normal subgroup graphs of alternating groups
Published 2022“…Some of the properties of a group are used to form the edges of the graph. A finite group can be represented in a graph by its subgroup structure. …”
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Conference or Workshop Item -
417
On subpolygroup commutativity degree of finite polygroups
Published 2023-08-01“…In this regard, we extend the concept of the subgroup commutativity degree of a finite group to the subpolygroup commutativity degree of a finite polygroup $ P $. …”
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418
QUASIRANDOM GROUP ACTIONS
Published 2016-01-01“…Let $G$ be a finite group acting transitively on a set $\unicode[STIX]{x1D6FA}$ . …”
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419
Note on structural properties of graphs
Published 2022-02-01“…In this paper, we establish sufficient and necessary conditions for the existence of abelian subgroups of maximal order of a finite group GG, by means of its commuting graph. The order of these subgroups attains the bound c=∣[x1]∣+⋯+∣[xm]∣c=| \left[{x}_{1}]| \hspace{-0.25em}+\cdots +\hspace{-0.25em}\hspace{0.33em}| \left[{x}_{m}]| , where [xi]\left[{x}_{i}] denotes the conjugacy class of xi{x}_{i} in GG and mm is the smallest integer jj such that ∣[x1]∣+⋯+∣[xj]∣≥∣CG(xj)∣| \left[{x}_{1}]| \hspace{-0.25em}+\cdots +| \left[{x}_{j}]| \ge | {C}_{G}\left({x}_{j})| , where CG(xj){C}_{G}\left({x}_{j}) is the centralizer of xj{x}_{j} in GG.…”
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420
The one-way communication complexity of group membership
Published 2010“…Here Alice receives, as input, a subgroup H of a finite group G; Bob receives an element x ∈ G. Alice is permitted to send a single message to Bob, after which he must decide if his input x is an element of H. …”
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