The Characterisation of Modular Group Algebras Having Unit Groups of Nilpotency Class 3

1995 ◽  
Vol 38 (1) ◽  
pp. 112-116 ◽  
Author(s):  
M. Anwar Rao ◽  
Robert Sandling
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Unit Group ◽  
Nilpotency Class ◽  
Group Algebras ◽  
Modular Group Algebra

AbstractThe unit group of the modular group algebra of a finite p-group in characteristic p is nilpotent. The p-groups for which it is of nilpotency class 3 were determined in work of Coleman, Passman, Shalev and Mann when p ≥ 3. We resolve the p = 2 case here which completes the classification.

scholarly journals The modular group algebra problem for groups of order p5

1996 ◽  
Vol 61 (2) ◽  
pp. 229-237 ◽  
Author(s):  
Mohamed A. M. Salim ◽  
Robert Sandling
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Nilpotency Class ◽  
Group Algebras ◽  
Modular Group Algebra

AbstractWe show that p-groups of order p5 are determined by their group algebras over the field of p elements. Many cases have been dealt with in earlier work of ourselves and others. The only case whose details remain to be given here is that of groups of nilpotency class 3 for p odd.

A NOTE ON THE NILPOTENCY CLASS OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA

2008 ◽  
Vol 108 (1) ◽  
pp. 65-68
Author(s):  
Francesco Catino ◽  
Salvatore Siciliano ◽  
Ernesto Spinelli
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Unit Group ◽  
Nilpotency Class ◽  
Modular Group Algebra

The Modular Group Algebra Problem for Small p-Groups Of Maximal Class

1996 ◽  
Vol 48 (5) ◽  
pp. 1064-1078
Author(s):  
Mohamed A. M. Salim ◽  
Robert Sandling
Keyword(s):  
Small Group ◽  
Group Algebra ◽  
Modular Group ◽  
Unit Group ◽  
Quotient Algebra ◽  
Group Algebras ◽  
Maximal Class ◽  
Modular Group Algebra

AbstractWe show that p-groups of maximal class and order p5 are determined by their group algebras over the field of p elements. The most important information requisite for the proof is obtained from a detailed study of the unit group of a quotient algebra of the group algebra, larger than the small group algebra.

Modular Group Algebras with Small Upper Lie Nilpotency Index

2020 ◽  
Vol 12 (1) ◽  
pp. 108-111
Author(s):  
Suchi Bhatt ◽  
Harish Chandra
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Group Algebras ◽  
Modular Group Algebra ◽  
Nilpotency Index

Let KG be the modular group algebra of a group G over a field K of characteristic p > 0. The classification of group algebras KG with upper Lie nilpotency index tL(KG) greater than or equal to |G′| – 13p + 14 have already been done. In this paper, our aim is to classify the group algebras KG for which tL(KG) = |G′| – 14p + 15.

scholarly journals Lie nilpotency index of a modular group algebra

2020 ◽  
pp. 2150129
Author(s):  
Meena Sahai ◽  
Bhagwat Sharan
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Index Formula ◽  
Group Algebras ◽  
Modular Group Algebra ◽  
Nilpotency Index

In this paper, we classify the modular group algebra [Formula: see text] of a group [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text] having upper Lie nilpotency index [Formula: see text] for [Formula: see text] and [Formula: see text]. Group algebras of upper Lie nilpotency index [Formula: see text] for [Formula: see text], have already been characterized completely.

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