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341
Graph related to cubed commutativity degree
Published 2020“…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}. …”
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342
Encoding and detecting properties in finitely presented groups
Published 2017“…In contrast, detectability in power subgroups fails for solvability of given derived length: we construct a finite group W such that W(<sup>2</sup>) and W(<sup>3</sup>) are metabelian but W has derived length 3. …”
Thesis -
343
Topics in additive combinatorics
Published 2016“…</p> <p>In Chapter 3 we prove that a randomly chosen subset of a finite group is a randomness extractor with high probability. …”
Thesis -
344
On the probability of zero divisor elements in group rings
Published 2022-12-01“…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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345
Structure of intersection graphs
Published 2021-12-01“…<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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346
The classification of symmetry protected topological phases of one-dimensional fermion systems
Published 2021-01-01“…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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347
Higher categorical symmetries and gauging in two-dimensional spin systems
Published 2024-04-01“…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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348
Drinfel’d double symmetry of the 4d Kitaev model
Published 2023-09-01“…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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349
GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS
Published 2020-01-01“…For a finite group $G$, let $d(G)$ denote the minimal number of elements required to generate $G$. …”
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350
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351
Stability and distributivity over orbital [infinity]-categories/
Published 2017Get full text
Thesis -
352
Product decompositions of quasirandom groups and a Jordan type theorem
Published 2007“…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 $|B| > |G| / k^{1/3}$ we have B^3 = G. …”
Journal article -
353
Degree exponent sum energy of commuting graph for dihedral groups
Published 2022“…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. …”
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354
The probability that two elements commute in some 2-generator 2-groups of nilpotency class 2
Published 2005“…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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Thesis -
355
The schur multipliers of certain bieberbach groups with abelian point groups
Published 2013“…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.…”
Conference or Workshop Item -
356
Some applications of metacyclic 2-groups of negative type
Published 2016“…The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. …”
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357
Group coloring via its geometric structures
Published 2021“…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. …”
Conference or Workshop Item -
358
Consistency relations of an extension polycyclic free abelian lattice group by quaternion point group
Published 2021“…An extension of a free abelian lattice group by finite group is a torsion free crystallographic group. …”
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Conference or Workshop Item -
359
t-Intuitionistic Fuzzification of Lagrange’s Theorem of t-Intuitionistic Fuzzy Subgroup
Published 2019-01-01“…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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360
Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters
Published 2023-02-01“…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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