On a two-fold cover 2.(2⁶˙G₂(2)) of a maximal subgroup of Rudvalis group Ru

Proyecciones (Antofagasta) ◽

10.22199/issn.0717-6279-4574 ◽

2021 ◽

Author(s):

Abraham Love Prins

Keyword(s):

Maximal Subgroup ◽

Simple Group ◽

Computer Algebra ◽

Computer Algebra System ◽

Schur Multiplier ◽

Split Extension ◽

Sporadic Simple Group ◽

Ordinary Character ◽

Factor Set ◽

Fold Cover

The Schur multiplier M(Ḡ1) ≅4 of the maximal subgroup Ḡ1 = 2⁶˙G₂(2)of the Rudvalis sporadic simple group Ru is a cyclic group of order 4. Hence a full representative group R of the type R = 4.(2⁶˙G₂(2)) exists for Ḡ1. Furthermore, Ḡ1 will have four sets IrrProj(Ḡ1;αi) of irreducible projective characters, where the associated factor sets α1, α2, α3 and α4, have orders of 1, 2, 4 and 4, respectively. In this paper, we will deal with a 2-fold cover 2. Ḡ1 of Ḡ1 which can be treated as a non-split extension of the form Ḡ = 27˙G2(2). The ordinary character table of Ḡ will be computed using the technique of the so-called Fischer matrices. Routines written in the computer algebra system GAP will be presented to compute the conjugacy classes and Fischer matrices of Ḡ and as well as the sizes of the sets |IrrProj(Hi; αi)| associated with each inertia factor Hi. From the ordinary irreducible characters Irr(Ḡ) of Ḡ, the set IrrProj(Ḡ1; α2) of irreducible projective characters of Ḡ1 with factor set α2 such that α22= 1, can be obtained.

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The Fischer–Clifford Matrices of a Maximal Subgroup of the Sporadic Simple Group of Held

Algebra Colloquium ◽

10.1142/s1005386707000132 ◽

2007 ◽

Vol 14 (01) ◽

pp. 135-142 ◽

Cited By ~ 2

Author(s):

Faryad Ali

Keyword(s):

Simple Group ◽

Computer Algebra ◽

Local Structure ◽

Computer Algebra System ◽

Conjugacy Classes ◽

Character Table ◽

Maximal Subgroups ◽

Split Extension ◽

Sporadic Simple Group ◽

Held Group

The Held group He discovered by Held [10] is a sporadic simple group of order 4030387200 = 210.33.52.73.17. The group He has 11 conjugacy classes of maximal subgroups as determined by Butler [5] and listed in the 𝔸𝕋𝕃𝔸𝕊. Held himself determined much of the local structure of He as well as the conjugacy classes of its elements. Thompson calculated the character table of He . In the present paper, we determine the Fischer–Clifford matrices and hence compute the character table of the non-split extension 3·S7, which is a maximal subgroups of He of index 226560 using the technique of Fischer–Clifford matrices. Most of the computations were carried out with the aid of the computer algebra system 𝔾𝔸ℙ.

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

Algebra Colloquium ◽

10.1142/s1005386710000386 ◽

2010 ◽

Vol 17 (03) ◽

pp. 389-414 ◽

Cited By ~ 4

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.

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NATURAL EXISTENCE PROOF FOR LYONS SIMPLE GROUP

Journal of Algebra and Its Applications ◽

10.1142/s021949880300043x ◽

2003 ◽

Vol 02 (03) ◽

pp. 277-315

Author(s):

GERHARD O. MICHLER ◽

MICHAEL WELLER ◽

KATSUSHI WAKI

Keyword(s):

Automorphism Group ◽

Simple Group ◽

Conjugacy Classes ◽

Existence Proof ◽

Sporadic Simple Group ◽

Character Tables ◽

The Given ◽

Fold Cover

In this article we give a self-contained existence proof for Lyons' sporadic simple group G by application of the first author's algorithm [18] to the given centralizer H ≅ 2A11 of a 2-central involution of G. It also yields four matrix generators of G inside GL 111 (5) which are given in Appendix A. From the subgroup U ≅ (3 × 2A8) : 2 of H ≅ 2A11, we construct a subgroup E of G which is isomorphic to the 3-fold cover 3McL: 2 of the automorphism group of the McLaughlin group McL. Furthermore, the character tables of E ≅ 3McL : 2 and G are determined and representatives of their conjugacy classes are given as short words in their generating matrices.

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ANATOMY OF THE MONSTER: II

Proceedings of the London Mathematical Society ◽

10.1112/s0024611502013357 ◽

2002 ◽

Vol 84 (3) ◽

pp. 581-598 ◽

Cited By ~ 13

Author(s):

SIMON P. NORTON ◽

ROBERT A. WILSON

Keyword(s):

Maximal Subgroup ◽

Simple Group ◽

Subject Classification ◽

Sporadic Simple Group ◽

Almost Simple Group ◽

Isomorphism Classes ◽

Current State ◽

Subgroup Problem

We describe the current state of progress on the maximal subgroup problem for the Monster sporadic simple group. Any unknown maximal subgroup is an almost simple group whose socle is in one of 19 specified isomorphism classes.2000 Mathematical Subject Classification:20D08.

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Recognizing M10 by spectrum in the class of all groups

International Journal of Algebra and Computation ◽

10.1142/s0218196714500088 ◽

2014 ◽

Vol 24 (02) ◽

pp. 113-119 ◽

Cited By ~ 2

Author(s):

Enrico Jabara ◽

Daria Lytkina ◽

Andrey Mamontov

Keyword(s):

Maximal Subgroup ◽

Simple Group ◽

Sporadic Simple Group ◽

Mathieu Group ◽

Locally Finite

We prove that a group with spectrum {1, 2, 3, 4, 5, 8} is locally finite and is isomorphic to M10, where M10 = A6 ⋅ 2 is the 3-transitive Mathieu group of degree 10, i.e. the corresponding maximal subgroup of the sporadic simple group M11.

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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