scholarly journals Conjugacy Class Representatives in the Monster Group

2005 ◽  
Vol 8 ◽  
pp. 205-216
Author(s):  
R. W. Barraclough ◽  
R. A. Wilson
Keyword(s):  
Conjugacy Class ◽  
Monster Group

AbstractThe paper describes a procedure for determining (up to algebraic conjugacy) the conjugacy class in which any element of the Monster lies, using computer constructions of representations of the Monster in characteristics 2 and 7. This procedure has been used to calculate explicit representatives for each conjugacy class.

scholarly journals On the Action of the Sporadic Simple Baby Monster Group on its Conjugacy Class 2B

2008 ◽  
Vol 11 ◽  
pp. 15-27 ◽  
Author(s):  
Jürgen Müller
Keyword(s):  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Endomorphism Ring ◽  
Free Action ◽  
Character Table ◽  
Computational Technique ◽  
Permutation Module ◽  
Monster Group ◽  
Multiplicity Free

AbstractWe determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster group B on its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 21+22.Co2. This is one of the first applications of a new general computational technique to enumerate big orbits.

scholarly journals The intersection graph of a finite simple group has diameter at most 5

2021 ◽  
Author(s):  
Saul D. Freedman
Keyword(s):  
Simple Group ◽  
Upper Bound ◽  
Finite Simple Group ◽  
Unitary Groups ◽  
Intersection Graph ◽  
Monster Group ◽  
Prime Dimension

AbstractLet G be a non-abelian finite simple group. In addition, let $$\Delta _G$$ Δ G be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of $$\Delta _G$$ Δ G has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.

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
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