scholarly journals Unit Groups of Semisimple Group Algebras of Abelianp-Groups over a Field

1997 ◽  
Vol 188 (2) ◽  
pp. 580-589 ◽  
Author(s):  
Nako A. Nachev ◽  
Todor Zh. Mollov
Keyword(s):  
Semisimple Group ◽  
Group Algebras

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

scholarly journals On Idempotents and the Number of Simple Components of Semisimple Group Algebras

2015 ◽  
Vol 19 (2) ◽  
pp. 315-333
Author(s):  
Gabriela Olteanu ◽  
Inneke Van Gelder
Keyword(s):  
Semisimple Group ◽  
Group Algebras

On the dimension of ideals in group algebras, and group codes

2020 ◽  
pp. 2250024
Author(s):  
E. J. García-Claro ◽  
H. Tapia-Recillas
Keyword(s):  
Minimum Distance ◽  
Semisimple Group ◽  
Group Algebras ◽  
Mds Codes ◽  
Hamming Weight ◽  
Group Codes ◽  
Minimal Polynomials ◽  
Principal Ideals ◽  
Regular Representations ◽  
Abelian Code

Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of semisimple group algebras, to compute, for any abelian code, an element with Hamming weight equal to its dimension. Finally, to get bounds on the minimum distance of certain MDS group codes. A relation between a class of group codes and MDS codes is presented. Examples illustrating the main results are provided.

STRUCTURE OF SOME CLASSES OF SEMISIMPLE GROUP ALGEBRAS OVER FINITE FIELDS

2014 ◽  
Vol 51 (6) ◽  
pp. 1605-1614 ◽  
Author(s):  
Neha Makhijani ◽  
Rajendra Kumar Sharma ◽  
J.B. Srivastava
Keyword(s):  
Finite Fields ◽  
Semisimple Group ◽  
Group Algebras

Good codes from metacyclic groups II

2020 ◽  
pp. 2250040
Author(s):  
Samir Assuena
Keyword(s):  
Finite Fields ◽  
Semisimple Group ◽  
Group Algebras ◽  
Dual Codes ◽  
Metacyclic Groups

In this paper, we consider semisimple group algebras [Formula: see text] of split metacyclic groups over finite fields. We construct left codes in [Formula: see text] in the case when the order [Formula: see text] is [Formula: see text], where [Formula: see text] and [Formula: see text] are different primes such that [Formula: see text] extend the construction described in a previous paper, determine their dual codes and find some good codes.

A note on normal complement problem

2017 ◽  
Vol 16 (01) ◽  
pp. 1750011 ◽  
Author(s):  
K. Kaur ◽  
M. Khan ◽  
T. Chatterjee
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Positive Characteristic ◽  
Unit Group ◽  
Semisimple Group ◽  
Group Algebras ◽  
Metacyclic Group ◽  
Infinite Class ◽  
Normal Complement ◽  
Characteristic 2

In this paper, we study the normal complement problem on semisimple group algebras and modular group algebras [Formula: see text] over a field [Formula: see text] of positive characteristic. We provide an infinite class of abelian groups [Formula: see text] and Galois fields [Formula: see text] that have normal complement in the unit group [Formula: see text] for semisimple group algebras [Formula: see text]. For metacyclic group [Formula: see text] of order [Formula: see text], where [Formula: see text] are distinct primes, we prove that [Formula: see text] does not have normal complement in [Formula: see text] for finite semisimple group algebra [Formula: see text]. Finally, we study the normal complement problem for modular group algebras over field of characteristic 2.

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