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381
The squared Commutativity degree of dihedral groups
Published 2016“…The commutativity degree of a finite group is the probability that a random pair of elements in the group commute. …”
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382
On the dominating number, independent number and the regularity of the relative co-prime graph of a group
Published 2017“…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. …”
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383
The energy of cayley graphs for a generating subset of the dihedral groups
Published 2019“…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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384
The energy of cayley graphs for symmetric groups of order 24
Published 2020“…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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385
Un método algoritmo para el cálculo del número baricéntrico de Ramsey para el grafo estrella
Published 2018-04-01“… 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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386
ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH
Published 2017-01-01“…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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387
Heights on stacks and a generalized Batyrev–Manin–Malle conjecture
Published 2023-01-01“…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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388
Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds
Published 2022-02-01“…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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389
Combinatoric topological string theories and group theory algorithms
Published 2022-10-01“…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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390
On finite totally $2$-closed groups
Published 2022-09-01“…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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391
Generalized symmetries and Noether’s theorem in QFT
Published 2022-08-01“…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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392
An approach to Quillen’s conjecture via centralisers of simple groups
Published 2021-01-01“…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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393
Representation rings for fusion systems and dimension functions
Published 2018“…We also give an application of our results to constructions of finite group actions on homotopy spheres.…”
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394
On the representations of disconnected reductive groups over F q
Published 2020“…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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Book chapter -
395
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396
Superinduction for pattern groups
Published 2015“…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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397
Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
Published 2014“…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 $\Gamma$. …”
Journal article -
398
Minimal generating pairs for permutation groups
Published 1980“…</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. …”
Thesis -
399
A new construction of compact 8-manifolds with holonomy Spin(7)
Published 1999“…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). …”
Journal article -
400
Compressive of the first disc Δı (t) of the commuting graph C (G, X) for elements of order three in symmetric groups
Published 2016“…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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