Lie Nilpotency Indices of Modular Group Algebras

被引：10

作者：

Bovdi, V. ^{[1
,2
]}

Srivastava, J. B. ^{[3
]}

机构：

[1] Univ Debrecen, Inst Math, H-4010 Debrecen, Hungary

[2] Coll Nyiregyhaza, Inst Math & Informat, H-4410 Nyiregyhaza, Hungary

[3] Indian Inst Technol, Dept Math, New Delhi 110016, India

来源：

ALGEBRA COLLOQUIUM | 2010年 / 17卷 / 01期

关键词：

group algebras; Lie nilpotency index; Lie dimension subgroups; GROUP-RINGS; UNITS;

D O I：

10.1142/S1005386710000040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that if KG is Lie nilpotent, then its tipper (or lower) Lie nilpotency index is at most vertical bar G'vertical bar +1, where vertical bar G'vertical bar is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal has already been determined. Here we determine G for which tipper (or lower) Lie nilpotency index is the next highest possible.

引用

页码：17 / 26

页数：10

共 18 条

[1]

[Anonymous], P LONDON MATH SOC

[2] LIE-NILPOTENCY INDEXES OF GROUP-ALGEBRAS [J].

BHANDARI, AK ;

PASSI, IBS .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1992, 24 :68-70

[3] Lie properties of the group algebra and the nilpotency class of the group of units [J].

Bovdi, AA ;

Kurdics, J .

JOURNAL OF ALGEBRA, 1999, 212 (01) :28-64

[4]

BOVDI AA, 1986, MAT SBORNIK, V171, P160

[5]

BOVDI AA, 1986, MAT SBORNIK, V171, P154

[6]

Bovdi V, 2004, PUBL MATH-DEBRECEN, V65, P243

[7]

Bovdi V., 2007, SCI MATH JPN, V65, P267

[8] Modular group algebras with almost maximal Lie nilpotency indices [J].

Bovdi, Victor ;

Juhasz, Tibor ;

Spinelli, Ernesto .

ALGEBRAS AND REPRESENTATION THEORY, 2006, 9 (03) :259-266

[9] THE CENTERS OF A RADICAL RING [J].

DU, XK .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1992, 35 (02) :174-179

[10] ON THE LIE IDEALS OF A RING [J].

GUPTA, N ;

LEVIN, F .

JOURNAL OF ALGEBRA, 1983, 81 (01) :225-231

← 1 2 →