Description of the first disc Δ1(t) of the commuting graph C(G, X) for elements of order three in symmetric groups by Nawawi, Athirah, Rowley, Peter J.

“…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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Tensor network approach to electromagnetic duality in (3+1)d topological gauge models by Clement Delcamp

“…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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Applications of conjunctive complex fuzzy subgroups to Sylow theory by Aneeza Imtiaz, Hanan Alolaiyan, Umer Shuaib, Abdul Razaq, Jia-Bao Liu

“…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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Topological Indices of the Relative Coprime Graph of the Dihedral Group by Abdul Gazir Syarifudin, Laila Maya Santi, Andi Rafiqa Faradiyah, Verrel Rievaldo Wijaya, Erma Suwastika

“…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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Fermionization of fusion category symmetries in 1+1 dimensions by Kansei Inamura

“…As concrete examples, we compute the fermionization of finite group symmetries, the symmetries of finite gauge theories, and duality symmetries. …”
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Semisimple and G-Equivariant Simple Algebras Over Operads by Etingof, Pavel

“…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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Generalized involution models for wreath products by Marberg, Eric Paul

“…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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Finite Dimensional Hopf Actions on Central Division Algebras by Cuadra-Diaz, Juan, Etingof, Pavel I

“…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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Finite symmetric tensor categories with the Chevalley property in characteristic 2 by Etingof, Pavel, Gelaki, Shlomo

“…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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Prospects for Quantum Equivariant Neural Networks by Castelazo, Grecia

“…We present efficient quantum algorithms for performing linear finite-group convolutions and cross-correlations on data stored as quantum states. …”
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Representation Theory in Complex Rank, I by Etingof, Pavel I.

“…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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A survey on elliptic curve cryptography by Mohamed, Mohamad Afendee

“…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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Cyclic intersection graph of subgroups of dihedral groups and its properties. by Alhubairah, Fozaiyah Ayed, Mohd. Ali, Nor Muhainiah, Erfanian, Ahmad

“…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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Multiplicative degree of some dihedral groups by Rhani, N. A., Ali, N. M. M., Sarmin, N. H., Erfanian, A., Hamid, M. A.

“…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. …”

Graph coloring using commuting order product prime graph by Bello, Muhammed, Mohd. Ali, Nor Muhainiah, Isah, Surajo Ibrahim

“…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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The application of GAP software in constructing the non-normal subgroup graphs of alternating groups by Rahin, N. F., Sarmin, Nor Haniza, Ilangovan, S.

“…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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On subpolygroup commutativity degree of finite polygroups by M. Al Tahan, Sarka Hoskova-Mayerova, B. Davvaz, A. Sonea

“…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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QUASIRANDOM GROUP ACTIONS by NICK GILL

“…Let $G$ be a finite group acting transitively on a set $\unicode[STIX]{x1D6FA}$ . …”
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Note on structural properties of graphs by Arreola-Bautista Luis D., Reyna Gerardo, Romero-Valencia Jesús, Sigarreta José M.

“…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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The one-way communication complexity of group membership by Le Gall, Francois, Tani, Seiichiro, Russell, Alexander, Aaronson, Scott

“…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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