The squared Commutativity degree of dihedral groups by Hamid, M. A., Ali, N. M. M., Sarmin, N. H., Erfanian, A., Manaf, F. N. A.

“…The commutativity degree of a finite group is the probability that a random pair of elements in the group commute. …”
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On the dominating number, independent number and the regularity of the relative co-prime graph of a group by Abd. Rhani, N., Mohd. Ali, N. M., Sarmin, N. H., Erfanian, A.

“…Let H be a subgroup of a finite group G. The co-prime graph of a group is defined as a graph whose vertices are elements of G and two distinct vertices are adjacent if and only if the greatest common divisor of order of x and y is equal to one. …”

The energy of cayley graphs for a generating subset of the dihedral groups by Ahmad Fadzil, Amira Fadina, Sarmin, Nor Haniza, Erfanian, Ahmad

“…Let G be a finite group and S be a subset of G where S does not include the identity of G and is inverse closed. …”
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The energy of cayley graphs for symmetric groups of order 24 by Fadzil, A. F. A., Sarmin, N. H., Erfanian, A.

“…A Cayley graph of a finite group G with respect to a subset S of G is a graph where the vertices of the graph are the elements of the group and two distinct vertices x and y are adjacent to each other if xy-1 is in the subset S. …”
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Un método algoritmo para el cálculo del número baricéntrico de Ramsey para el grafo estrella by Felicia Villarroel, J. Figueroa, H. Márquez, A. Anselmi

“… Let G be an abelian finite group and H be a graph. A sequence in G, with length al least two, is barycentric if it contains an ”average” element of its terms. …”
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ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH by ANDREA LUCCHINI, CLAUDE MARION

“…Given a finite group $G$ , the generating graph $\unicode[STIX]{x1D6E4}(G)$ of $G$ has as vertices the (nontrivial) elements of $G$ and two vertices are adjacent if and only if they are distinct and generate $G$ as group elements. …”
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Heights on stacks and a generalized Batyrev–Manin–Malle conjecture by Jordan S. Ellenberg, Matthew Satriano, David Zureick-Brown

“…We explain how to compute this height for various stacks of interest (for instance: classifying stacks of finite groups, symmetric products of varieties, moduli stacks of abelian varieties, weighted projective spaces). …”
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Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds by Samperton, Eric G.

“…In forthcoming work with Segovia we give a complete homological characterization of those finite groups admitting such a non-extending action, as well as more examples and non-examples. …”
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Combinatoric topological string theories and group theory algorithms by Sanjaye Ramgoolam, Eric Sharpe

“…Abstract A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on Dijkgraaf-Witten theory of flat G-bundles on surfaces. …”
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On finite totally $2$-closed groups by Abdollahi, Alireza, Arezoomand, Majid, Tracey, Gareth

“…Finally, we prove that a finite insoluble totally $2$-closed group $G$ of minimal order with non-trivial Fitting subgroup has shape $Z\cdot X$, with $Z=Z(G)$ cyclic, and $X$ is a finite group with a unique minimal normal subgroup, which is nonabelian.…”
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Generalized symmetries and Noether’s theorem in QFT by Valentin Benedetti, Horacio Casini, Javier M. Magán

“…These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether’s theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). …”
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An approach to Quillen’s conjecture via centralisers of simple groups by Kevin Iván Piterman

“…For any given subgroup H of a finite group G, the Quillen poset ${\mathcal {A}}_p(G)$ of nontrivial elementary abelian p-subgroups is obtained from ${\mathcal {A}}_p(H)$ by attaching elements via their centralisers in H. …”
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Representation rings for fusion systems and dimension functions by Yalçın, Ergün, Reeh, Sune Nikolaj Precht

“…We also give an application of our results to constructions of finite group actions on homotopy spheres.…”
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On the representations of disconnected reductive groups over F q by Lusztig, George

“…One of the main tools in the study of representations of the finite group G(Fq) over a field of characteristic zero is the use of certain varieties Xw (see [DL1]) on which G(Fq) acts (here w is a Weyl group element). …”
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On trigonometric and elliptic Cherednik algebras by Ma, Xiaoguang, Ph. D. Massachusetts Institute of Technology

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Superinduction for pattern groups by Marberg, Eric, Thiem, Nathaniel

“…It is well known that the representation theory of the finite group of unipotent upper-triangular matrices U[subscript n] over a finite field is a wild problem. …”
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Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields by Chan, S, Hollmann, H, Pasechnik, D

“…A maximal minor $M$ of the Laplacian of an $n$-vertex Eulerian digraph $\Gamma$ gives rise to a finite group $\mathbb{Z}^{n-1}/\mathbb{Z}^{n-1}M$ known as the sandpile (or critical) group $S(\Gamma)$ of $\Gamma$. …”

Minimal generating pairs for permutation groups by Conder, M, Conder, Marston Donald Edward

“…</p><p>The case k = 7 is of particular importance. Any finite group which can be generated by elements x, y satisfying</p><p>x² = y³ = (xy)⁷ = 1</p><p>is called a <em>Hurwitz</em>group, and gives rise to a compact Riemann surface of which it is a maximal automorphism group. …”

A new construction of compact 8-manifolds with holonomy Spin(7) by Joyce, D

“…In a previous paper (Invent. math. 123 (1996), 507-552) the author constructed the first examples of compact 8-manifolds with holonomy Spin(7), by resolving orbifolds T^8/G, where T^8 is the 8-torus and G a finite group of automorphisms of T^8. This paper describes a different construction of compact 8-manifolds with holonomy Spin(7). …”

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

“…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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