Theoretical Researches about u-Maximal Subgroups and Its Applications in Charactering IntuG by Li Zhang, Zheng-Qun Cai

“…Let G be a finite group and u be the class of all finite supersoluble groups. …”
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Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums by Zoltán Kádár, Annalisa Marzuoli, Mario Rasetti

“…Equivalence of the previous models in the ground state is shown in case of the honeycomb lattice and the gauge group being a finite group by means of the well-known duality transformation between the group algebra and the spin network basis of lattice gauge theory. …”
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C⁎-Basic Construction from the Conditional Expectation on the Drinfeld Double by Qiaoling Xin, Lining Jiang, Tianqing Cao

“…Let D(G) be the Drinfeld double of a finite group G and D(G;H) be the crossed product of C(G) and CH, where H is a subgroup of G. …”
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The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras by Dinh Trung Hoa, Toan Minh Ho, Hiroyuki Osaka

“…As an application, let A be a simple unital C*-algebra with the LP property, α an action of a finite group G onto Aut(A). If α has the Rokhlin property in the sense of Izumi, then the fixed point algebra AG and the crossed product algebra A ⋊α G have the LP property. …”
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(SPT-)LSM theorems from projective non-invertible symmetries by Salvatore D. Pace, Ho Tat Lam, and Ömer M. Aksoy

“…This model is specified by a finite group $G$ and enjoys a projective $\mathsf{Rep}(G)× Z(G)$ and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. …”
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Essential dimension of symmetric groups in prime characteristic by Edens, Oakley, Reichstein, Zinovy

“…Finding this number is a long-standing open problem, originating in the work of Felix Klein, long before essential dimension of a finite group was formally defined. We now know that $\operatorname{ed}_k(\operatorname{S}_n)$ lies between $\lfloor n/2 \rfloor $ and $n-3$ for each $n \geqslant 5$ and any field $k$ of characteristic different from $2$. …”
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Equivariant geometry of singular cubic threefolds by Ivan Cheltsov, Yuri Tschinkel, Zhijia Zhang

“…We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.…”
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Pinned-flags of some operations on fuzzy subgroups by B. B. Makamba, V. Murali

“…Fuzzy subgroups of finite groups have been treated recently using the concept of pinned-flags. …”
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Eigenvalues of Relatively Prime Graphs Connected with Finite Quasigroups by Muhammad Nadeem, Nwazish Ali, Hafiz Muhammad Bilal, Md. Ashraful Alam, M. I. Elashiry, Kholood Alnefaie

“…Many studies have focused on the spectral properties of simple graphs connected to associative algebras like finite groups and rings, but the same research direction remains unexplored for loop groups and quasigroups. …”
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Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques by A. El-Mesady, Omar Bazighifan

“…Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments in designing an experiment to permit effective statistical analysis of results, they encode the incidence structure of finite geometries, they encapsulate the structure of finite groups and more general algebraic objects known as quasigroups, and they produce optimal density error-correcting codes. …”
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