Product-Free Subsets of Groups, Then and Now by Kedlaya, Kiran S.

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Reductions of Tensor Categories Modulo Primes by Gelaki, Shlomo, Etingof, Pavel I.

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On Two Properties of Shunkov Group by A.A. Shlepkin, I. V. Sabodakh

“…The group $G$ is called Shunkov group if for any finite subgroup $H$ of $G$ in the quotient group $N_G(H)/H$, any two conjugate elements of prime order generate a finite group. When studying the Shunkov group $G$, a situation often arises when it is necessary to move to the quotient group of the group $G$ by some of its normal subgroup $N$. …”
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On Residual Separability of Subgroups in Split Extensions by A. A. Krjazheva

“…Recall also that the subgroup H of a group G is called finitely separable if for every element g of G, which does not belong to the subgroup H, there exists a homomorphism of G on a finite group in which the image of an element g does not belong to the image of the subgroup H. …”
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Informationally Complete Characters for Quark and Lepton Mixings by Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Klee Irwin

“…A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters <inline-formula> <math display="inline"> <semantics> <mi>κ</mi> </semantics> </math> </inline-formula> of a finite group <i>G</i>. Here, we introduce a <i>d</i>-dimensional Hilbert space with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mi>c</mi> <mi>c</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, the number of conjugacy classes of <i>G</i>. …”
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On two generation methods for the simple linear group $PSL(3,7)$ by Thekiso Seretlo

“…A finite group $G$ is said to be \textit{$(l,m, n)$-generated}, if it is a quotient group of the triangle group $T(l,m, n) = \left<x, y, z|x^{l} = y^{m} = z^{n} = xyz = 1\right>.$ In [J. …”
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Double coset Markov chains by Persi Diaconis, Arun Ram, Mackenzie Simper

“…Let G be a finite group. Let $H, K$ be subgroups of G and $H \backslash G / K$ the double coset space. …”
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Recognition of the symplectic simple group $ PSp_4(p) $ by the order and degree prime-power graph by Chao Qin, Yu Li, Zhongbi Wang, Guiyun Chen

“…Let $ G $ be a finite group, $ \operatorname{cd}(G) $ the set of all irreducible character degrees of $ G $, and $ \rho(G) $ the set of all prime divisors of integers in $ \operatorname{cd}(G) $. …”
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A deterministic algorithm for the discrete logarithm problem in a semigroup by Tinani Simran, Rosenthal Joachim

“…The discrete logarithm problem (DLP) in a finite group is the basis for many protocols in cryptography. …”
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Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases by A. Perez-Lona, D. Robbins, E. Sharpe, T. Vandermeulen, X. Yu

“…We discuss how ordinary G orbifolds for finite groups G are a special case of the construction, corresponding to the fusion category Vec(G) = Rep(ℂ[G]*). …”
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Stable Grothendieck rings of wreath product categories by Ryba, Christopher

“…We discuss some applications when $$ {\mathcal {R}} $$ R is the group algebra of a finite group, and some results about stable Kronecker coefficients. …”
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Stable Grothendieck rings of wreath product categories by Ryba, Christopher

“…We discuss some applications when $$ {\mathcal {R}} $$ R is the group algebra of a finite group, and some results about stable Kronecker coefficients. …”
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The Quantum Double Model with Boundary: Condensations and Symmetries by Beigi, Salman, Shor, Peter W., Whalen, Daniel

“…Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. …”
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Theory of interacting topological crystalline insulators by Isobe, Hiroki, Fu, Liang

“…We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group Z[subscript 8]. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap eight flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. …”
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The width of verbal subgroups in profinite groups by Simons, N, Nicholas James Simons

“…As a corollary we note that our approach also proves that every word has finite width in a polycyclic-by-finite group (which is not profinite). As a supplementary result we show that for finitely generated closed subgroups H and K of a profinite group the commutator subgroup [H,K] is closed, and give examples to show that various hypotheses are necessary. …”

Identical relations in simple groups by Oates, S

“…Neumann considers the question of whether the identical relations of a given variety (and, in particular, the variety generated by a finite group) are finitely based. He shows this to be true for a variety of abelian groups, and R. …”

Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry by Naren Manjunath, Maissam Barkeshli

“…An important role is played by a finite group grading on Burgers vectors, which depends on the point group symmetry of the lattice.…”
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Quantizing Euclidean Motions via Double-Coset Decomposition by Christian W&#xfc;lker, Sipu Ruan, Gregory S. Chirikjian

“…More specifically, a very efficient, equivolumetric quantization of spatial motion can be defined using the group-theoretic concept of a double-coset decomposition of the form Γ\SE(3)/Δ, where Γ is a Sohncke space group and Δ is a finite group of rotational symmetries such as those of the icosahedron. …”
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Equivariant noncommutative motives by Trigo Neri Tabuada, Goncalo Jorge

“…Given a finite group G, we develop a theory of G-equivariant noncommutative motives. …”
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Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons by Kong, Liang, Lan, Tian, Wen, Xiao-Gang

“…In this paper, following a new line of thinking, we find that in 3+1D the classification is much simpler than it was thought to be; we propose a partial classification of topological orders for 3+1D bosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair (G,ω_{4}): a finite group G and its group 4-cocycle ω_{4}∈H^{4}[G;U(1)] (up to group automorphisms). …”
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