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.

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.

scholarly journals Rationality of the generalized binomial coefficients for a multiplicity free action

2000 ◽  
Vol 68 (3) ◽  
pp. 387-410 ◽  
Author(s):  
Chal Benson ◽  
Gail Ratcliff
Keyword(s):  
Vector Space ◽  
Canonical Basis ◽  
Free Action ◽  
Homogeneous Component ◽  
Binomial Coefficients ◽  
Invariant Polynomials ◽  
Finite Dimensional ◽  
Multiplicity Free ◽  
Lie Subgroup ◽  
Generalized Binomial Coefficients

AbstractLetVbe a finite dimensional Hermitian vector space andKbe a compact Lie subgroup ofU(V) for which th representation ofKonC[V] is multiplicity free. One obtains a canonical basis {pα} for the spaceC[VR]kofK-invariant polynomials on VRand also a basis {q's. The polynomialpα's yields the homogeneous component of highest degree inqα. The coefficient that express theqα's in terms of thepβ's are the generalized binomial coeffficients of Yan. The main result in this paper shows tht these numbers are rational.

scholarly journals On the Moment Map of a Multiplicity Free Action

1996 ◽  
Vol 71 (1) ◽  
pp. 107-110 ◽  
Author(s):  
Andrzej Daszkiewicz ◽  
Tomasz Przebinda
Keyword(s):  
Free Action ◽  
Moment Map ◽  
The Moment ◽  
Multiplicity Free

scholarly journals Nilpotent injectors in finite groups

1985 ◽  
Vol 32 (2) ◽  
pp. 293-297 ◽  
Author(s):  
Peter Förster
Keyword(s):  
Finite Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Finite Groups ◽  
Nilpotent Groups ◽  
Fitting Class ◽  
Basic Properties ◽  
A Finite Group ◽  
Class F

Nilpotent injectors exist in all finite groups.For every Fitting class F of finite groups (see [2]), InjF(G) denotes the set of all H ≤ G such that for each N ⊴ ⊴ G , H ∩ N is an F -maximal subgroup of N (that is, belongs to F and i s maximal among the subgroups of N with this property). Let W and N* denote the Fitting class of all nilpotent and quasi-nilpotent groups, respectively. (For the basic properties of quasi-nilpotent groups, and of the N*-radical F*(G) of a finite group G3 the reader is referred to [5].,X. %13; we shall use these properties without further reference.) Blessenohl and H. Laue have shown in CJ] that for every finite group G, InjN*(G) = {H ≤ G | H ≥ F*(G) N*-maximal in G} is a non-empty conjugacy class of subgroups of G. More recently, Iranzo and Perez-Monasor have verified InjN(G) ≠ Φ for all finite groups G satisfying G = CG(E(G))E(G) (see [6]), and have extended this result to a somewhat larger class M of finite groups C(see [7]). One checks, however, that M does not contain all finite groups; for example, S5 ε M.

scholarly journals Characterization of a family of simple groups by their character table

1977 ◽  
Vol 24 (3) ◽  
pp. 296-304 ◽  
Author(s):  
Marcel Herzog ◽  
David Wright
Keyword(s):  
Conjugacy Class ◽  
Simple Group ◽  
Character Table ◽  
Simple Groups

AbstractThe paper establishes a method for bounding the 2-rank of a simple group with one conjugacy class of involutions, by means of its character table. For many groups of 2-rank ≦ 4, this bound is shown to be exact. The main result is that the simple groups G2(q),(q,6) = 1, are characterized bv their character table.

scholarly journals The Character Table of a Maximal Subgroup of the Monster

2007 ◽  
Vol 10 ◽  
pp. 161-175 ◽  
Author(s):  
R. W. Barraclough ◽  
R. A. Wilson
Keyword(s):  
Maximal Subgroup ◽  
Character Table ◽  
Group 3

AbstractWe calculate the character table of the maximal subgroup of the Monster N(3B) isomorphic to a group of shape 3+1+12 · 2 · Suz: 2, and also of the group 31+12 : 6 · Suz · 2, which has the former as a quotient. The strategy is to induce characters from the inertia groups in 31+12 : 6 · Suz : 2 of characters of 31+12. We obtain the quotient map to N(3B) computationally, and our careful concrete approach allows us to produce class fusions between our tables and various tables in the GAP library.

scholarly journals Fischer-Clifford Matrices and Character Table of the Maximal Subgroup (29:(L3(4)):2 of U6(2):2

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Abraham Love Prins ◽  
Ramotjaki Lucky Monaledi
Keyword(s):  
Automorphism Group ◽  
Maximal Subgroup ◽  
Unitary Group ◽  
Character Table ◽  
Split Extension ◽  
Parent Group ◽  
Extension Group ◽  
Clifford Theory

The automorphism group U6(2):2 of the unitary group U6(2)≅Fi21 has a maximal subgroup G¯ of the form (29:(L3(4)):2 of order 20643840. In this paper, Fischer-Clifford theory is applied to the split extension group G¯ to construct its character table. Also, class fusion from G¯ into the parent group U6(2):2 is determined.

Degrees, class sizes and divisors of character values

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Patrick X. Gallagher
Keyword(s):  
Finite Group ◽  
Conjugacy Class ◽  
Class Size ◽  
Spherical Functions ◽  
Character Degree ◽  
Character Table ◽  
Arithmetic Property ◽  
Conjugacy Class Size ◽  
A Finite Group ◽  
Central Characters

Abstract.In the character table of a finite group there is a tendency either for the character degree to divide the conjugacy class size or the character value to vanish. There is also a partial divisibility where the determinant of the character is not 1. There are versions of these depending on a subgroup, based on an arithmetic property of spherical functions which generalizes the integrality of the values of the characters and the central characters.

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 The Moment Map for a Multiplicity Free Action

1994 ◽  
Vol 31 (2) ◽  
pp. 185-191 ◽  
Author(s):  
Chal Benson ◽  
Joe Jenkins ◽  
Ronald L. Lipsman ◽  
Gail Ratcliff
Keyword(s):  
Free Action ◽  
Moment Map ◽  
The Moment ◽  
Multiplicity Free
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