The Lyons group has no distance-transitive representation

1993 ◽  
pp. 355-358 ◽  
Author(s):  
L. H. Soicher
Keyword(s):  
Transitive Representation ◽  
Lyons Group

scholarly journals Completing the Brauer Trees for the Sporadic Simple Lyons Group

2002 ◽  
Vol 5 ◽  
pp. 18-33 ◽  
Author(s):  
Jürgen Müller ◽  
Max Neunhöffer ◽  
Frank Röhr ◽  
Robert Wilson
Keyword(s):  
Representation Theory ◽  
Computer Algebra ◽  
Computer Algebra Systems ◽  
Computational Representation ◽  
Lyons Group

AbstractIn this paper, the Brauer trees are completed for the sporadic simple Lyons group Ly in characteristics 37 and 67. The results are obtained using tools from computational representation theory—in particular, a new condensation technique—and with the assistance of the computer algebra systems MeatAxe and GAP.

The maximal subgroups of the Lyons group

1985 ◽  
Vol 97 (3) ◽  
pp. 433-436 ◽  
Author(s):  
Robert A. Wilson
Keyword(s):  
Simple Group ◽  
Maximal Subgroups ◽  
Subgroup Structure ◽  
Image Position ◽  
Lyons Group

In this paper we complete the work begun in [2] on the subgroup structure of the Lyons simple group Ly of order

Clebsch–Gordan decomposition for transitive representations

1985 ◽  
Vol 63 (8) ◽  
pp. 1061-1064 ◽  
Author(s):  
B. Lulek ◽  
T. Lulek ◽  
R. Chatterjee ◽  
J. Biel
Keyword(s):  
Finite Group ◽  
Direct Product ◽  
Fibre Bundle ◽  
Canonical Realization ◽  
A Finite Group ◽  
Method Of Evaluation ◽  
Transitive Representation

The method of evaluation of Clebsch–Gordan coefficients to calculate the direct product of transitive representations for a finite group is developed. This procedure is based on the Mackey theorem and on the canonical realization of transitive representations. It is shown that the Clebsch–Gordan decomposition is associated with a natural interpretation of an orbit of a resultant transitive representation and it is analogous to a fibre bundle with the fibration being determined by constituent transitive representations.

COVERINGS OF LINKS AND A GENERALIZATION OF RILEY’S CONJECTURE B

1996 ◽  
Vol 05 (04) ◽  
pp. 463-488 ◽  
Author(s):  
F. GONZÁLEZ-ACUÑA ◽  
ARTURO RAMÍREZ
Keyword(s):  
Symmetric Group ◽  
Branched Covers ◽  
Torus Knot ◽  
Group Information ◽  
Transitive Representation

Let k be a knot in S3, ψ: π1(S3–k)→Zα1 * Zα2 an epimorphism sending a meridian to an element of length 2 and ω: Zα1 * Zα2→Sσ a transitive representation into a symmetric group. Information is given (in Theorem B##) on the homologies of the unbranched and branched covers associated to ωψ which generalizes a conjecture of Riley. When k is a torus knot these homologies are actually computed.

A Note on Groups of Ree Type

1973 ◽  
Vol 16 (3) ◽  
pp. 451-452 ◽  
Author(s):  
Peter Lorimer
Keyword(s):  
Ree Group ◽  
Transitive Representation

The nonsolvable R-groups as defined by Walter [3] are groups of orders (q3+l)q3(q — 1), q = 32n+1, n ≥ 0. These are the groups of Ree type discussed by Ward [4] together with the Ree group R(3) of order 28.27.2. The R-group with parameter q has a doubly transitive representation of degree q3+1 but in this note we will prove that it cannot contain a sharply doubly transitive subset.

A CHARACTERISTIC 5 IDENTIFICATION OF THE LYONS GROUP

2004 ◽  
Vol 69 (01) ◽  
pp. 128-140 ◽  
Author(s):  
CHRISTOPHER PARKER ◽  
PETER ROWLEY
Keyword(s):  
Lyons Group

A root system for the Lyons group

1989 ◽  
Vol 283 (2) ◽  
pp. 285-299
Author(s):  
Wolfram Neutsch ◽  
Werner Meyer
Keyword(s):  
Root System ◽  
Lyons Group

ON A NEW APPROACH TO THE DUAL SYMMETRIC INVERSE MONOID $\mathcal{I}_{X}^{\ast}$

2007 ◽  
Vol 17 (03) ◽  
pp. 567-591 ◽  
Author(s):  
VICTOR MALTCEV
Keyword(s):  
Inverse Semigroup ◽  
Cross Section ◽  
Inverse Monoid ◽  
Finite Sets ◽  
New Approach ◽  
Generating Set ◽  
Maximal Subsemigroups ◽  
Symmetric Inverse Semigroup ◽  
Transitive Representation ◽  
Symmetric Inverse Monoid

We construct the inverse partition semigroup[Formula: see text], isomorphic to the dual symmetric inverse monoid[Formula: see text], introduced in [6]. We give a convenient geometric illustration for elements of [Formula: see text]. We describe all maximal subsemigroups of [Formula: see text] and find a generating set for [Formula: see text] when X is finite. We prove that all the automorphisms of [Formula: see text] are inner. We show how to embed the symmetric inverse semigroup into the inverse partition one. For finite sets X, we establish that, up to equivalence, there is a unique faithful effective transitive representation of [Formula: see text], namely to [Formula: see text]. Finally, we construct an interesting [Formula: see text]-cross-section of [Formula: see text], which is reminiscent of [Formula: see text], the [Formula: see text]-cross-section of [Formula: see text], constructed in [4].

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