Black Box Groups

Şükrü YALÇINKAYA

Makale detayları

Black Box Groups

Yazarlar:

Şükrü YALÇINKAYA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2007 Vol.31 Issue Suppl, pp.171-210

Belge Tipi:

Makale

Yayın Tarihi:

11/2006

Belge Dili:

Türkçe

Document ID (Org No.):

2000748508

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

We propose a uniform approach for recognizing all black box  groups of Lie type which is based on the analysis of the structure of  the centralizers of involutions.  Our approach can be viewed as a  computational version of the classification of the finite simple  groups.  We present an algorithm which constructs a long root  SL2(q)-subgroup in a finite simple group of Lie type of odd  characteristic, then we use the Aschbacher's Classical Involution  Theorem'' as a model in the recognition algorithm and we construct all  root SL2(q)-subgroups corresponding to the nodes in the extended  Dynkin diagram, that is, we construct the extended Curtis - Phan -  Tits system of the finite simple groups of Lie type of odd  characteristic.  In particular, we construct all subsystem subgroups  which can be read from the extended Dynkin diagram.  We also present  an algorithm which determines whether the p-core (or unipotent  radical'') Op(G) of a black box group G is trivial or not, where  G/Op(G) is a finite simple classical group of odd characteristic p,  answering a well-known question of Babai and Shalev.

 

We propose a uniform approach for recognizing all black box  groups of Lie type which is based on the analysis of the structure of  the centralizers of involutions.  Our approach can be viewed as a  computational version of the classification of the finite simple  groups.  We present an algorithm which constructs a long root  SL2(q)-subgroup in a finite simple group of Lie type of odd  characteristic, then we use the Aschbacher's Classical Involution  Theorem'' as a model in the recognition algorithm and we construct all  root SL2(q)-subgroups corresponding to the nodes in the extended  Dynkin diagram, that is, we construct the extended Curtis - Phan -  Tits system of the finite simple groups of Lie type of odd  characteristic.  In particular, we construct all subsystem subgroups  which can be read from the extended Dynkin diagram.  We also present  an algorithm which determines whether the p-core (or unipotent  radical'') Op(G) of a black box group G is trivial or not, where  G/Op(G) is a finite simple classical group of odd characteristic p,  answering a well-known question of Babai and Shalev.

Makale detayları

Black Box Groups

Yazarlar:

Şükrü YALÇINKAYA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2007 Vol.31 Issue Suppl, pp.171-210

Belge Tipi:

Makale

Yayın Tarihi:

11/2006

Belge Dili:

Türkçe

Document ID (Org No.):

2000748508

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Turk. J. Math.

31

(2007)

171-210. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.31

iss.Suppl.

Sayı

Makale detayları

Black Box Groups

Yazarlar: Şükrü YALÇINKAYA

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2007 Vol.31 Issue Suppl, pp.171-210

Belge Tipi: Makale

Yayın Tarihi: 11/2006

Belge Dili: Türkçe

Document ID (Org No.): 2000748508

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Turk. J. Math.

31

(2007)

171-210. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.31

iss.Suppl.

Sayı

Yazarlar:

Şükrü YALÇINKAYA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2007 Vol.31 Issue Suppl, pp.171-210

Belge Tipi:

Makale

Yayın Tarihi:

11/2006

Belge Dili:

Türkçe

Document ID (Org No.):

2000748508

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098