Modular group algebras with small Lie nilpotency indices

Siwach, Reetu; Sharma, Rajendra K.; Sahai, Meena

doi:10.1142/s1793557116500807

Cited by 8 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [3], Bovdi and Kurdics discussed the upper and lower Lie nilpotency index of a modular group algebra of metabelian group G and determine the nilpotency class of the group of units. Recently, we have some results on classification of Lie nilpotent group algebras of Lie nilpotency index upto 14 (see [2,8,22,24]). Furthermore, group algebras with minimal Lie nilpotency index p + 1 have been classified by Sharma and Bist [21].…”

Section: Introductionmentioning

confidence: 99%

A note on modular group algebras with upper Lie nilpotency indices

Bhatt

Chandra

2022

ADM

View full text Add to dashboard Cite

Let KG be the modular group algebra of anarbitrary group G over a field K of characteristic p>0. In thispaper we give some improvements of upper Lie nilpotency indext L(KG) of the group algebra KG. It can be seen that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is atleast p+1. In this way the classification of group algebras KG with next upper Lie nilpotency indext L(KG) up to 9p−7 have alreadybeen classified. Furthermore, we give a complete classification ofmodular group algebraKGfor which the upper Lie nilpotency index is 10p−8.

show abstract

Section: Introductionmentioning

confidence: 99%

A note on modular group algebras with upper Lie nilpotency indices

Bhatt

Chandra

2022

ADM

View full text Add to dashboard Cite

show abstract

“…In [3], Bovdi and Kurdics discussed the upper and lower Lie nilpotency index of a modular group algebra of metabelian group G and determine the nilpotency class of the group of units. Recently, we have some results on classification of Lie nilpotent group algebras of Lie nilpotency index upto 14 (see [2,8,21,23]). Furthermore, group algebras with minimal Lie nilpotency index p + 1 have been classified by Sharma and Bist [20].…”

Section: Introductionmentioning

confidence: 99%

On the Lie nilpotency index of modular group algebras

Bhatt,

Chandra

2020

Preprint

View full text Add to dashboard Cite

Let KG be the modular group algebra of an arbitrary group G over a field K of characteristic p > 0. It is seen that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least p + 1. The classification of group algebras KG with upper Lie nilpotency index t L (KG) upto 9p − 7 have already been determined. In this paper, we classify the modular group algebra KG for which the upper Lie nilpotency index is 10p − 8.

show abstract