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

Abstract The Schur multiplier M(Ḡ 1) ≅ 4 of the maximal subgroup Ḡ 1 = 26· G 2(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 Ḡ 1. Furthermore, Ḡ...

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Auteur principal:	Prins,Abraham Love
Langue:	English
Publié:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Sujets:	Non-split extension Projective character table Factor set Schur multiplier Representation group Inertia factor groups Fischer matrices
Accès en ligne:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401011
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spelling	oai:scielo:S0716-091720210004010112021-08-12On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group RuPrins,Abraham Love Non-split extension Projective character table Factor set Schur multiplier Representation group Inertia factor groups Fischer matrices Abstract The Schur multiplier M(Ḡ 1) ≅ 4 of the maximal subgroup Ḡ 1 = 26· G 2(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 Ḡ 1. Furthermore, Ḡ 1 will have four sets IrrP roj(Ḡ 1, 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. Ḡ 1 of Ḡ 1 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(Ḡ 1, α2) of irreducible projective characters of Ḡ 1 with factor set α2 such that α2 2 = 1, can be obtained.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.4 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401011en10.22199/issn.0717-6279-4574
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Non-split extension Projective character table Factor set Schur multiplier Representation group Inertia factor groups Fischer matrices
spellingShingle	Non-split extension Projective character table Factor set Schur multiplier Representation group Inertia factor groups Fischer matrices Prins,Abraham Love On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru
description	Abstract The Schur multiplier M(Ḡ 1) ≅ 4 of the maximal subgroup Ḡ 1 = 26· G 2(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 Ḡ 1. Furthermore, Ḡ 1 will have four sets IrrP roj(Ḡ 1, 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. Ḡ 1 of Ḡ 1 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(Ḡ 1, α2) of irreducible projective characters of Ḡ 1 with factor set α2 such that α2 2 = 1, can be obtained.
author	Prins,Abraham Love
author_facet	Prins,Abraham Love
author_sort	Prins,Abraham Love
title	On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru
title_short	On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru
title_full	On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru
title_fullStr	On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru
title_full_unstemmed	On a two-fold cover 2.(26·G 2 (2)) of a maximal subgroup of Rudvalis group Ru
title_sort	on a two-fold cover 2.(26·g 2 (2)) of a maximal subgroup of rudvalis group ru
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401011
work_keys_str_mv	AT prinsabrahamlove onatwofoldcover226g22ofamaximalsubgroupofrudvalisgroupru
_version_	1718439913335029760

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

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