A note on the degree bounds of the invariant ring by Yang Zhang, Jizhu Nan

“…Let $ G = C_p\times H $ be a finite group, where $ C_p $ is a cyclic group of prime order $ p $ and $ H $ is a $ p^{\prime} $-group. …”
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Simulations of Cayley graphs of dihedral group by Farhan Mohammad, John Peter, Silaban Denny Riama

“…Let Γ be a finite group with identity element e and let S ⊆ Γ − {e} which is inverse-closed, i.e., S = S−1 := {s−1 : s ∈ S}. …”
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Using Group Theory to Obtain Eigenvalues of Nonsymmetric Systems by Symmetry Averaging by Marion L. Ellzey

“…If the Hamiltonian in the time independent Schrödinger equation, HΨ = EΨ, is invariant under a group of symmetry transformations, the theory of group representations can help obtain the eigenvalues and eigenvectors of H. A finite group that is not a symmetry group of H is nevertheless a symmetry group of an operator Hsym projected from H by the process of symmetry averaging. …”
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A REFINED WARING PROBLEM FOR FINITE SIMPLE GROUPS by MICHAEL LARSEN, PHAM HUU TIEP

“…Further results concerning thin bases of $G$ of order $2$ are established for any finite group and for any compact Lie group $G$.…”
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Rigid automorphisms of linking systems by George Glauberman, Justin Lynd

“…In a second result, we show that if an automorphism of a finite group G restricts to the identity on the centric linking system for G, then it is of $p'$-order modulo the group of inner automorphisms, provided G has no nontrivial normal $p'$-subgroups. …”
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Weights in a Benson-Solomon block by Justin Lynd, Jason Semeraro

“…When the pair arises from a genuine block of a finite group algebra in characteristic p, the number of conjugacy classes of weights is supposed to be the number of simple modules in the block. …”
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New Zémor-Tillich Type Hash Functions Over GL2 (𝔽pn) by Tomkins Hayley, Nevins Monica, Salmasian Hadi

“…We present a large class of new Zémor-Tillich type hash functions whose target space is the finite group GL2(𝔽pn) for any prime p and power n. To do so, we use a novel group-theoretic approach that uses Tits’ “Ping-Pong Lemma” to outline conditions under which a set of matrices in PGL2(𝔽p((x))) generates a free group. …”
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Structure of blocks with normal defect and abelian $p'$ inertial quotient by David Benson, Radha Kessar, Markus Linckelmann

“…Let $kGe$ be a block of a group algebra of a finite group G, with normal defect group P and abelian $p'$ inertial quotient L. …”
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Arithmetic properties and decomposability of Jacobians by Park, Soohyun, S.M. Massachusetts Institute of Technology

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On the rank varieties and Jordan types of a class of simple modules by Wang, Jialin

“…Fix a finite group G and an algebraically closed field F of characteristic p. …”
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Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields by Chan, SH, Hollmann, HDL, Pasechnik, DV

“…<p>A maximal minor M of the Laplacian of an n-vertex Eulerian digraph Γ gives rise to a finite group Zn−1/Zn−1M known as the sandpile (or critical) group S(Γ) of Γ. …”

Profinite rigidity, Kleinian groups, and the cofinite Hopf property by Bridson, MR, Reid, AW

“…If H has finite index in Γ, then there is a finite group onto which H maps but Γ does not. These results streamline the existing proofs that there exist full-sized groups that are profinitely rigid in the absolute sense. …”

Counting primes, groups and manifolds by Goldfeld, D, Lubotzky, A, Nikolov, N, Pyber, L

“…The proofs use techniques from number theory, algebraic groups, finite group theory and combinatorics.…”

Sylow subgroups of index 2 in their normalizers by Smith, S

“…<p>The following theorem is proved:</p> <p><strong>Theorem</strong> Let G be a finite group, P a Sylow p-subgroup of G, p odd. Suppose</p> <ol type="1"> <li>|N(P)/P⋅C(P)| = 2;</li> <li>cl(P) ≤ 2 .…”

The exceptional holonomy groups and calibrated geometry 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. …”

Direct products and profinite completions by Nikolov, N, Segal, D

“…Let G be a finitely generated residually finite group and A a finitely generated normal subgroup. …”

On diameter of subgraphs of commuting graph in symplectic group for elements of order three by Suzila Mohd Kasim, Athirah Nawawi

“…Suppose G be a finite group and X be a subset of G. The commuting graph, denoted by C(G,X), is a simple undirected graph, where X ⊂ G being the set of vertex and two distinct vertices x,y ∈ X are joined by an edge if and only if xy = yx. …”
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On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups by Romdhini, Mamika Ujianita, Nawawi, Athirah

“…The non-commuting graph, denoted by , is defined on a finite group , with its vertices are elements of excluding those in the center of . …”

Zoology of atlas-groups: dessins d’enfants, finite geometries and quantum commutation by Planat, Miche, Zainuddin, Hishamuddin

“…Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. …”
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The cubed commutativity degree of dihedral groups by Hamid, M. A., Ali, N. M. M., Sarmin, N. H., Erfanian, A.

“…Let G be a finite group. The commutativity degree of a group is the probability that a random pair of elements in the group commute. …”