TY - JOUR

T1 - Modular group algebras with almost maximal Lie nilpotency indices

AU - Bovdi, Victor

AU - Juhász, Tibor

AU - Spinelli, Ernesto

N1 - Funding Information:
The research was supported by OTKA No. T 037202, No. T 038059 and Italian National Research Project “Group Theory and Application.”

PY - 2006

Y1 - 2006

N2 - 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 upper (and lower) Lie nilpotency index is at most |G'|+1 where |G'| is the order of the commutator subgroup. The authors previously determined those groups G for which this index is maximal and here they determine the groups G for which it is 'almost maximal', that is, it takes the next highest possible value, namely |G'|-p+2.

AB - 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 upper (and lower) Lie nilpotency index is at most |G'|+1 where |G'| is the order of the commutator subgroup. The authors previously determined those groups G for which this index is maximal and here they determine the groups G for which it is 'almost maximal', that is, it takes the next highest possible value, namely |G'|-p+2.

KW - Dimensional subgroups

KW - Group algebras

KW - Lie nilpotency indices

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U2 - 10.1007/s10468-006-9022-5

DO - 10.1007/s10468-006-9022-5

M3 - Article

AN - SCOPUS:33846994359

SN - 1386-923X

VL - 9

SP - 259

EP - 266

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 3

ER -