Commutativity Degree of Certain Finite AC-Groups by Azizollah Azad, Sakineh Rahbariyan

“…For a finite group G, the probability of two elements of G that commute is the commutativity degree of G denoted by P(G). …”
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Polynomial composites and certain types of fields extensions by Ł. Matysiak

“…Moreover, in this paper we show that any finite group is a Galois group of some field extensions and present the inverse Galois problem solved.…”
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$p$-parts of co-degrees of irreducible characters by Bahramian, Roya, Ahanjideh, Neda

“…For a character $\chi $ of a finite group $G$, the co-degree of $\chi $ is $\chi ^c(1)=\frac{[G:\ker \chi ]}{\chi (1)}$. …”
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Hamiltonian Normal Cayley Graphs by Montellano-Ballesteros Juan José, Arguello Anahy Santiago

“…A variant of the Lovász Conjecture on hamiltonian paths states that every finite connected Cayley graph contains a hamiltonian cycle. Given a finite group G and a connection set S, the Cayley graph Cay(G, S) will be called normal if for every g ∈ G we have that g−1Sg = S. …”
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On unit P-Groups in Group Algebra by ALAA .A. AWAD

“…Abstract:The aim of this paper we have define the group of units U(F(G)), where F(G) is the group algebra with G is finite group over a field F. Now if char F=0 and G nonabelian or F is a nonabsolute field of characterstic > 0 and G/ O (G) is nonabelian, then it is well known that the group of unit U(K[G]) contains a nonabelain P-group.There for we will prove that there are two cyclic subgroups X and Y of G of prime power order and units uX U(K[X]) and uY U(K[X]) such that (uX,uY) contain nonabelian P-subgroups in linear group…”
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Characterization of some alternating groups by order and largest element order by Ali Mahmoudifar, Ayoub Gharibkhajeh

“…The prime graph (or Gruenberg-Kegel graph) of a finite group is a well-known graph. In this paper, first, we investigate the structure of the finite groups with a non-complete prime graph. …”
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On the Non-Inverse Graph of a Group by Amreen Javeria, Naduvath Sudev

“…Let (G, *) be a finite group and S = {u ∈ G|u ≠ u−1}, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S. …”
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A generalization of Taketa's theorem on $\rm M$-groups II by Zeinab Akhlaghi

“…In the recent paper [A generalization of Taketa's theorem on $M$-groups, Quaestiones Mathematicae, (2022)], we give an upper bound $5/2$ for the average of non-monomial character degrees of a finite group $G$, denoted by $\mathrm{acd}_{nm}(G)$, which guarantees the solvability of $G$. …”
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Javier de Lucas and the ethics of immigration by Francisco Javier Laporta San Miguel

“…However, the questions that all of this asks us are not capable of avoiding the affirmation that the idea of distributive justice presupposes a finite group of individuals among whom to distribute, and that of self-determination, a right of the group to organize that distribution by itself. same. …”
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Completeness for concrete near-rings by Aichinger, E, Masulovic, D, Poschel, R, Wilson, J

“…In this paper a completeness criterion for near-rings over a finite group is derived using techniques from clone theory. …”

Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz by Hausel, T, Rodriguez-Villegas, F

“…We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. …”

Constructing compact manifolds with exceptional holonomy by Joyce, D

“…The simplest such constructions work by using techniques from complex geometry and Calabi-Yau analysis to resolve the singularities of a torus orbifold T^7/G or T^8/G, for G a finite group preserving a flat G2 or Spin(7)-structure on T^7 or T^8. …”

Dimer and polymer metamaterials with alternating electric and magnetic coupling by Radkovskaya, A, Sydoruk, O, Tatartschuk, E, Gneiding, N, Stevens, C, Edwards, D, Shamonina, E

“…The resulting dispersion characteristics are shown to be radically different from the classical acoustic and optical branches: the upper branch is a forward wave and the lower branch is a backward wave, and even the gap between the two pass bands may disappear yielding infinite phase, finite group-velocity wave. The theory is confirmed both by simulations and experiments. © 2011 American Physical Society.…”

Fibre products, non-positive curvature, and decision problems by Baumslag, G, Bridson, M, Miller, C, Short, H

“…We give a criterion for fibre products to be finitely presented and use it as the basis of a construction that encodes the pathologies of finite group presentations into pairs of groups P ⊂ G where G is a product of hyperbolic groups and P is a finitely presented subgroup. …”

Mixed Hodge polynomials of character varieties by Hausel, T, Rodriguez-Villegas, F

“…We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. …”

On the group rings of Abelian minimax groups by Segal, D

“…Recall that the divisible abelian groups with min are direct products of finitely many quasicyclic groups (groups of type <em>C_p∞</em>, for various primes <em>p</em>), and that an abelian group with min is the direct product of a divisible one with a finite group...</p>…”

Degree sum energy of non-commuting graph for dihedral groups by Romdhini, Mamika Ujianita, Nawawi, Athirah

“…For a finite group G, let Z(G) be the centre of G. Then the non-commuting graph on G, denoted by ΓG, has G\Z(G) as its vertex set with two distinct vertices vp and vq joined by an edge whenever vpvq ≠ vqvp. …”

Maximum and minimum degree energy of commuting graph for dihedral groups by Romdhini, Mamika Ujianita, Nawawi, Athirah

“…If is a finite group and is the centre of , then the commuting graph for , denoted by , has as its vertices set with two distinct vertices and are adjacent if . …”

The disc structures of commuting involution graphs for certain simple groups by Mohd Kasim, Suzila, Nawawi, Athirah, Said Husain, Sharifah Kartini, Ibrahim, Siti Nur Iqmal

“…Suppose is a finite group and is a subset of. The commuting graph on the set , whose vertex set with any two vertices connected by an edge if and only if they commute. …”
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A general case of the commutativity degree of nilpotent p-groups of class two by Abd. Manaf, F. N., Sarmin, N. H., Mohd. Ali, N. M., Erfanian, A., Ghouchan, M. F. D.

“…Given a finite group, the commutativity degree of the group is defined as the probability that two elements of the group, chosen randomly with replacement, commute. …”