A NOTE ON THE DERIVED LENGTH OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA

2002 ◽  
Vol 30 (10) ◽  
pp. 4905-4913 ◽  
Author(s):  
Czesław Bagiński
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Unit Group ◽  
Derived Length ◽  
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.

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.

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]

On the order of unitary subgroup of the modular group algebra 𝔽2kD2N

2015 ◽  
Vol 14 (08) ◽  
pp. 1550129 ◽  
Author(s):  
Neha Makhijani ◽  
R. K. Sharma ◽  
J. B. Srivastava
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Dihedral Group ◽  
Group Of Units ◽  
Modular Group Algebra ◽  
Canonical Involution ◽  
Unitary Subgroup

Let 𝔽qD2N be the group algebra of D2N, the dihedral group of order 2N, over 𝔽q = GF (q). In this paper, we compute the order of the unitary subgroup of the group of units of 𝔽2kD2N with respect to the canonical involution ∗.

ON THE CENTER OF THE MODULAR GROUP ALGEBRA OF A FINITE p-GROUP

2014 ◽  
Vol 13 (04) ◽  
pp. 1350127
Author(s):  
CZESŁAW BAGIŃSKI ◽  
JÁNOS KURDICS
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Conjugacy Classes ◽  
Characteristic P ◽  
Cyclic Groups ◽  
Modular Group Algebra ◽  
Index 2 ◽  
Zero Multiplication

Let G be a finite nonabelian p-group and F a field of characteristic p and let [Formula: see text] be the subalgebra spanned by class sums [Formula: see text], where C runs over all conjugacy classes of noncentral elements of G. We show that all finite p-groups are subgroups and homomorphic images of p-groups for which [Formula: see text]. We also give the description of abelian-by-cyclic groups for which [Formula: see text] is an algebra with zero multiplication or is nil of index 2.

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