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 50 条

[31] On the nilpotency and decomposition of Lie-type algebras
N. A. Koreshkov
Mathematical Notes, 2007, 82 : 321 - 331
[32] On the nilpotency and decomposition of lie-type algebras
Koreshkov, N. A.
MATHEMATICAL NOTES, 2007, 82 (3-4) : 321 - 331
[33] Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
Singh, Dev Karan
Pandey, Mani Shankar
Kumar, Shiv Datt
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2024, 74 (01) : 283 - 299
[34] Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
Dev Karan Singh
Mani Shankar Pandey
Shiv Datt Kumar
Czechoslovak Mathematical Journal, 2024, 74 : 283 - 299
[35] LIE NILPOTENCY OF GROUP-RINGS
GIAMBRUNO, A
SEHGAL, SK
COMMUNICATIONS IN ALGEBRA, 1993, 21 (11) : 4253 - 4261
[36] Nilpotency indices of the radicals of finite p-solvable group algebras.: II
Ninomiya, Y
COMMUNICATIONS IN ALGEBRA, 2002, 30 (06) : 2843 - 2851
[37] On the lower Lie nilpotency index of a group algebra
Sahai, Meena
Sharan, Bhagwat
QUAESTIONES MATHEMATICAE, 2021, 44 (10) : 1347 - 1354
[38] On the cohomology of modular Lie algebras
Feldvoss, Joerg
LIE ALGEBRAS, VERTEX OPERATOR ALGEBRAS AND THEIR APPLICATIONS, 2007, 442 : 89 - 113
[39] THE CHARACTERIZATION OF MODULAR GROUP-ALGEBRAS HAVING UNIT GROUPS OF NILPOTENCY CLASS-3
RAO, MA
SANDLING, R
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1995, 38 (01): : 112 - 116
[40] Lie properties of the group algebra and the nilpotency class of the group of units
Bovdi, AA
Kurdics, J
JOURNAL OF ALGEBRA, 1999, 212 (01) : 28 - 64

← 1 2 3 4 5 →