Graph related to cubed commutativity degree by Mohd. Ali, N. M., Abdul Hamid, M., Sarmin, N. H., Erfanian, A.

“…Let G be a finite group and T3(G) be the set of third power of commuting element in G i.e T3(G) = {x∈G|(xg)3 = (gx)3}. …”

Encoding and detecting properties in finitely presented groups by Gardam, G

“…In contrast, detectability in power subgroups fails for solvability of given derived length: we construct a finite group W such that W(²) and W(³) are metabelian but W has derived length 3. …”

Topics in additive combinatorics by Mrazovic, R

“…</p> <p>In Chapter 3 we prove that a randomly chosen subset of a finite group is a randomness extractor with high probability. …”

On the probability of zero divisor elements in group rings by Haval Mohammed Salih

“…We denote by $P(RG)$ the probability that the product of two randomly chosen elements of a finite group ring $RG$ is zero‎. ‎We show that $P(RG)<\frac{1}{4}$ if and only if $RG\ncong \mathbb{Z}_2C_2,\mathbb{Z}_3C_2‎, ‎\mathbb{Z}_2C_3$‎. ‎…”
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Structure of intersection graphs by Haval M. Mohammed Salih, Sanaa M. S. Omer

“…<p style="text-align: left;" dir="ltr"> Let <em>G</em> be a finite group and let <em>N</em> be a fixed normal subgroup of <em>G</em>.  …”
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The classification of symmetry protected topological phases of one-dimensional fermion systems by Chris Bourne, Yoshiko Ogata

“…We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group G. This index takes values in $\mathbb {Z}_2 \times H^1(G,\mathbb {Z}_2) \times H^2(G, U(1)_{\mathfrak {p}})$ with a generalised Wall group law under stacking. …”
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Higher categorical symmetries and gauging in two-dimensional spin systems by Clement Delcamp, Apoorv Tiwari

“…We exemplify this approach by specialising to certain finite group generalisations of the transverse-field Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.…”
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Drinfel’d double symmetry of the 4d Kitaev model by Hank Chen

“…Abstract Following the general theory of categorified quantum groups developed by the author previously, we construct the Drinfel’d double 2-bialgebra associated to a finite group N = G 0. For N = ℤ 2, we explicitly compute the braided 2-categories of 2-representations of certain version of this Drinfel’d double 2-bialgebra, and prove that they characterize precisely the 4d toric code and its spin-ℤ 2 variant. …”
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GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS by ANDREA LUCCHINI, CLAUDE MARION, GARETH TRACEY

“…For a finite group $G$, let $d(G)$ denote the minimal number of elements required to generate $G$. …”
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Parametrized higher category theory by Shah, Jay (Jay Hungfai Gautam)

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Stability and distributivity over orbital [infinity]-categories/ by Nardin, Denis, Ph. D. Massachusetts Institute of Technology

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Product decompositions of quasirandom groups and a Jordan type theorem by Nikolov, N, Pyber, L

“…We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If k is the minimal degree of a representation of the finite group G, then for every subset B of G with $|B| &gt; |G| / k^{1/3}$ we have B^3 = G. …”

Degree exponent sum energy of commuting graph for dihedral groups by Romdhin, Mamika Ujianita, Nawawi, Athirah, Chen, Chuei Yee

“…For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. …”

The probability that two elements commute in some 2-generator 2-groups of nilpotency class 2 by Mohamad, Mohd. Sham

“…Erdos and Turan have introduced the determination of the abelianness of a finite group for symmetric groups, finite groups and finite rings in 1968. …”
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The schur multipliers of certain bieberbach groups with abelian point groups by Mat Hassim, Hazzirah Izzati, Sarmin, Nor Haniza, Mohd. Ali, Nor Muhainiah, Masri, Rohaidah, Mohd. Idrus, Nor'ashiqin

“…It is an extension of a free abelian group L of finite rank by a finite group P. Here, L is known as the lattice group while P is the point group of the Bieberbach group.…”

Some applications of metacyclic 2-groups of negative type by Saleh Omer, Sanaa Mohamed, Sarmin, Nor Haniza, Erfanian, Ahmad

“…The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. …”

Group coloring via its geometric structures by Muhammed Bello, Muhammed Bello, Mohd. Ali, Nor Muhainiah

“…Meanwhile an edge coloring of Γ is an assignment of colors to E(Γ), so that no any two incident edges share the same color. Let G be a finite group, an order product prime graph of G, is a graph Γopp(G), having the elements of G as its vertices and two vertices are adjacent if and only if the product of their order is a prime power. …”

Consistency relations of an extension polycyclic free abelian lattice group by quaternion point group by Mohammad, Siti Afiqah, Sarmin, Nor Haniza, Mat Hassim, Hazzirah Izzati

“…An extension of a free abelian lattice group by finite group is a torsion free crystallographic group. …”
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t-Intuitionistic Fuzzification of Lagrange&#x2019;s Theorem of t-Intuitionistic Fuzzy Subgroup by Hanan Alolaiyan, Umer Shuaib, Laila Latif, Abdul Razaq

“…In this study, we propose the concept of t-intuitionistic fuzzy order of an element of a t-intuitionistic fuzzy subgroup (t-IFSG) of a finite group and examine different important algebraic properties of this phenomena. …”
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Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters by Neda Ahanjideh

“…For a character $ \chi $ of a finite group $ G $, the number $ \chi^c(1)=\frac{[G:{\rm ker}\chi]}{\chi(1)} $ is called the co-degree of $ \chi $. …”
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