scholarly journals The infimum of Lipschitz constants in the conjugacy class of an interval map

2018 ◽  
Vol 147 (1) ◽  
pp. 255-269 ◽  
Author(s):  
Jozef Bobok ◽  
Samuel Roth
Keyword(s):  
Conjugacy Class ◽  
Interval Map ◽  
Lipschitz Constants

scholarly journals A NONDEGENERATE EXCHANGE MOVE ALWAYS PRODUCES INFINITELY MANY NONCONJUGATE BRAIDS

2019 ◽  
pp. 1-4
Author(s):  
TETSUYA ITO
Keyword(s):  
Conjugacy Class

We show that if a link $L$ has a closed $n$ -braid representative admitting a nondegenerate exchange move, an exchange move that does not obviously preserve the conjugacy class, $L$ has infinitely many nonconjugate closed $n$ -braid representatives.

ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES

2021 ◽  
pp. 1-5
Author(s):  
SH. RAHIMI ◽  
Z. AKHLAGHI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Regular Graph ◽  
Simple Graph ◽  
Conjugacy Classes ◽  
A Finite Group

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

Prime Divisors ofp-regular Conjugacy Class Sizes

2015 ◽  
Vol 43 (8) ◽  
pp. 3365-3371 ◽  
Author(s):  
Yang Liu ◽  
Ziqun Lu
Keyword(s):  
Conjugacy Class ◽  
Conjugacy Class Sizes ◽  
Prime Divisors

Conjugacy class numbers and π-subgroups

2021 ◽  
Vol 311 (1) ◽  
pp. 135-164
Author(s):  
Gunter Malle ◽  
Gabriel Navarro ◽  
Geoffrey R. Robinson
Keyword(s):  
Conjugacy Class ◽  
Class Numbers

THE CONJUGACY CLASSES OF SOME FINITE METABELIAN GROUPS AND THEIR RELATED GRAPHS

2016 ◽  
Vol 79 (1) ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Ain Asyikin Ibrahim ◽  
Alia Husna Mohd Noor ◽  
Sanaa Mohamed Saleh Omer
Keyword(s):  
Graph Theory ◽  
Conjugacy Class ◽  
Dihedral Group ◽  
Clique Number ◽  
Conjugacy Classes ◽  
Quaternion Group ◽  
Metabelian Groups ◽  
Dominating Number ◽  
Graph Properties ◽  
Class Graph

In this paper, the conjugacy classes of three metabelian groups, namely the Quasi-dihedral group, Dihedral group and Quaternion group of order 16 are computed. The obtained results are then applied to graph theory, more precisely to conjugate graph and conjugacy class graph. Some graph properties such as chromatic number, clique number, dominating number and independent number are found.   

scholarly journals Nesting Monte Carlo for high-dimensional non-linear PDEs

2018 ◽  
Vol 24 (4) ◽  
pp. 225-247 ◽  
Author(s):  
Xavier Warin
Keyword(s):  
Monte Carlo ◽  
Deep Learning ◽  
High Dimension ◽  
Analytical Solutions ◽  
New Method ◽  
Computational Time ◽  
High Dimensional ◽  
Learning Methods ◽  
Lipschitz Constants ◽  
Linear Pdes

Abstract A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Depending on the type of non-linearity, different schemes are proposed and theoretically studied: variance error are given and it is shown that the bias of the schemes can be controlled. The limitation of the method is that the maturity or the Lipschitz constants of the non-linearity should not be too high in order to avoid an explosion of the computational time. Many numerical results are given in high dimension for cases where analytical solutions are available or where some solutions can be computed by deep-learning methods.

scholarly journals ON REGULAR GROUPS AND FIELDS

2014 ◽  
Vol 79 (3) ◽  
pp. 826-844 ◽  
Author(s):  
TOMASZ GOGACZ ◽  
KRZYSZTOF KRUPIŃSKI
Keyword(s):  
Conjugacy Class ◽  
Classical Group ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Generic Type ◽  
Common Generalization ◽  
Counter Example ◽  
Minimal Groups ◽  
Unbounded Orbit

AbstractRegular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenP(n)has unbounded orbit under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable.

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