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On Two Properties of Shunkov Group
Published 2021-03-01“…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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424
On Residual Separability of Subgroups in Split Extensions
Published 2015-08-01“…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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425
Informationally Complete Characters for Quark and Lepton Mixings
Published 2020-06-01“…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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426
On two generation methods for the simple linear group $PSL(3,7)$
Published 2023-02-01“…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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427
Double coset Markov chains
Published 2023-01-01“…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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428
Recognition of the symplectic simple group $ PSp_4(p) $ by the order and degree prime-power graph
Published 2024-01-01“…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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429
A deterministic algorithm for the discrete logarithm problem in a semigroup
Published 2022-07-01“…The discrete logarithm problem (DLP) in a finite group is the basis for many protocols in cryptography. …”
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430
Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases
Published 2024-02-01“…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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431
Stable Grothendieck rings of wreath product categories
Published 2021“…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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432
Stable Grothendieck rings of wreath product categories
Published 2021“…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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433
The Quantum Double Model with Boundary: Condensations and Symmetries
Published 2012“…Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. …”
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434
Theory of interacting topological crystalline insulators
Published 2015“…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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435
The width of verbal subgroups in profinite groups
Published 2009“…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. …”
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436
Identical relations in simple groups
Published 1963“…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. …”
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437
Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
Published 2021-01-01“…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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438
Quantizing Euclidean Motions via Double-Coset Decomposition
Published 2019-01-01“…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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439
Equivariant noncommutative motives
Published 2018“…Given a finite group G, we develop a theory of G-equivariant noncommutative motives. …”
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440
Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons
Published 2018“…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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