The nilpotency class of the unit group of a modular group algebra I

1990 ◽  
Vol 70 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Aner Shalev
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Algebra I ◽  
Unit Group ◽  
Nilpotency Class ◽  
Modular Group Algebra

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.

The nilpotency class of the unit group of a modular group algebra II

1990 ◽  
Vol 70 (3) ◽  
pp. 267-277 ◽  
Author(s):  
Avinoam Mann ◽  
Aner Shalev
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Unit Group ◽  
Nilpotency Class ◽  
Algebra Ii ◽  
Modular Group Algebra

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

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.

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.

Units of commutative group rings over polynomial ring

2018 ◽  
Vol 13 (01) ◽  
pp. 2050021
Author(s):  
S. Kaur ◽  
M. Khan
Keyword(s):  
Abelian Group ◽  
Finite Field ◽  
Polynomial Ring ◽  
Group Algebra ◽  
Modular Group ◽  
Finite Abelian Group ◽  
Unit Group ◽  
Group Rings ◽  
Modular Group Algebra ◽  
Univariate Polynomial

In this paper, we obtain the structure of the normalized unit group [Formula: see text] of the modular group algebra [Formula: see text], where [Formula: see text] is a finite abelian group and [Formula: see text] is the univariate polynomial ring over a finite field [Formula: see text] of characteristic [Formula: see text]

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