Complete group of central units in some group rings over Z and Z[θp] Vitor Araujo Garcia, Raul Antonio Ferraz Communications in Algebra, 2024 In the present work, we contribute with new results that enabled us to give an explicit description of the groups of central units of integral group rings and group rings with coefficients in Z[θ], for certain groups G, where θ is a p− primitive root of unity and p is a prime number. In particular, we find a set of generators for the case where G is the Heisenberg Group.
Units in some group rings over the ring of p-cyclotomic integers Vitor Araujo Garcia, Raul Antonio Ferraz Journal of Algebra and Its Applications, 2023 Describing the group of units of a group ring is a classical problem. Let [Formula: see text] be a rational prime number. We set [Formula: see text] a primitive root of unity of order [Formula: see text], [Formula: see text] the ring of [Formula: see text]-cyclotomic integers, [Formula: see text] a finite abelian [Formula: see text]-group and [Formula: see text] the group of the units [Formula: see text] of [Formula: see text] such that [Formula: see text], where [Formula: see text] is the augmentation map. We will prove that all the elements of the group [Formula: see text] arise from the units of the group ring [Formula: see text], where [Formula: see text] is the cyclic group of order [Formula: see text]. As an application, we describe explicitly the group of units of the group ring [Formula: see text] when [Formula: see text] is an elementary abelian [Formula: see text]-group and [Formula: see text] is a regular prime number.
One-weight codes in some classes of group rings Raul Antonio Ferraz, Ruth Nascimento Ferreira Applicable Algebra in Engineering Communications and Computing, 2021 Let $${\\mathbb {F}}_q$$ be a finite field with q elements and G be a finite abelian group. In this work we gave conditions to ensure that a code in $${\\mathbb {F}}_qG$$ is a one-weight code in the case when G is a cyclic group with n elements, such that $${\\text {gcd}}(n,q) = 1$$ , and also when G is an abelian group.
Central units in some integral group rings Vitor Araujo Garcia, Raul Antonio Ferraz Communications in Algebra, 2021 Let G be a finite group and ZG be the integral group ring of G. We denote by U1(ZG) the group of normalized units of ZG; that is, the units which have augmentation 1, and by Z(U1(ZG)) the group of normalized central units. Many articles have been written describing the groups U1(ZG) and Z(U1(ZG)) for certain groups G. In this work, we will describe the group of normalized central units of some integral group rings by applying the idea presented in an article by Ferraz and Simón to a wider variety of groups, and we will study some examples of groups that can be treated with this method: metacyclic groups of type Cqm⋊Cpn; some metacyclic p-groups; some metabelian p-groups and some generalized dihedral groups.
Central Units in ℤCp, q Raul Antonio Ferraz, Juan Jacobo Simón Communications in Algebra, 2016 Let Cp, q be the semi-direct product of a cyclic group of order q by a cyclic group of order p, and ℤCp, q the integral group ring of Cp, q. In this article, firstly, we describe the group of normalized central units of ℤCp, q as a direct product of two subgroups that we call units of first kind and of second kind. For a class of prime numbers that we call good primes, we construct a multiplicatively independent set which generates the group of units of first kind. Finally, we construct a set of multiplicatively independent units which generates the units of second kind for a larger class of primes.
Complete group of central units in some group rings over and VA Garcia, RA Ferraz Communications in Algebra 52 (12), 5352-5363 , 2024 2024
Twisted group algebras of Abelian groups A Duarte, RA Ferraz, CP Milies Finite Fields and Their Applications 95, 102386 , 2024 2024 Citations: 7
Units in some group rings over the ring of p-cyclotomic integers VA Garcia, RA Ferraz Journal of Algebra and Its Applications 22 (05), 2350104 , 2023 2023 Citations: 1
Central units in some integral group rings VA Garcia, RA Ferraz Communications in Algebra 49 (9), 4000-4015 , 2021 2021 Citations: 1
Essential idempotents in group algebras and coding theory RA Ferraz, CP Milies Indian Journal of Pure and Applied Mathematics 52 (3), 747-760 , 2021 2021 Citations: 3
One-weight codes in some classes of group rings RA Ferraz, RN Ferreira Applicable Algebra in Engineering, Communication and Computing 32, 299-309 , 2021 2021
Left ideals of matrix rings and error-correcting codes RA Ferraz, CP Milies, E Taufer Applicable Algebra in Engineering, Communication and Computing 32, 311-320 , 2021 2021 Citations: 3
Essential idempotents and simplex codes G Chalom, RA Ferraz, CP Milies Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2 … , 2017 2017 Citations: 15
Minimal ideals in finite abelian group algebras and coding theory G Chalom, RA Ferraz, M Guerreiro São Paulo Journal of Mathematical Sciences 10 (2), 321-340 , 2016 2016 Citations: 2
Central Units in ℤ C p , q RA Ferraz, JJ Simón Communications in Algebra 44 (5), 2264-2275 , 2016 2016 Citations: 4
Units of (C p× C 2) and (C p× C 2× C 2) RA Ferraz, R Marcuz Communications in Algebra 44 (2), 851-872 , 2016 2016
Units of ℤ( C p × C 2 ) and ℤ( C p × C 2 × C 2 ) RA Ferraz, R Marcuz Communications in Algebra 44 (2), 851-872 , 2016 2016 Citations: 2
Units of Z (Cp× C2) and Z (Cp× C2× C2) RA Ferraz, RRM Silva Communications in Algebra 44 (2), 851-872 , 2016 2016 Citations: 8
Units of ℤ C p n RA Ferraz, PM Kitani Communications in Algebra 43 (11), 4936-4950 , 2015 2015 Citations: 6
-Equivalence in Group Algebras and Minimal Abelian Codes RA Ferraz, M Guerreiro, CP Milies IEEE Transactions on Information Theory 60 (1), 252-260 , 2013 2013 Citations: 23
Minimal Binary Abelian Codes of length G Chalom, RA Ferraz, M Guerreiro, CP Milies arXiv preprint arXiv:1205.5699 , 2012 2012 Citations: 8
Minimal codes in binary abelian group algebras M Guerreiro, RA Ferraz, CP Milies 2011 IEEE Information Theory Workshop, 225-228 , 2011 2011 Citations: 5
Some classes of semisimple group (and loop) algebras over finite fields RA Ferraz, EG Goodaire, CP Milies Journal of Algebra 324 (12), 3457-3469 , 2010 2010 Citations: 15
Semisimple group codes and dihedral codes FS Dutra, RA Ferraz, CP Milies Algebra and Discrete Mathematics, 28-48 , 2009 2009 Citations: 57
Units of ZCP RA Ferraz Contemporary Mathematics 499, 107 , 2009 2009 Citations: 16
MOST CITED SCHOLAR PUBLICATIONS
Idempotents in group algebras and minimal abelian codes RA Ferraz, CP Milies Finite Fields and Their Applications 13 (2), 382-393 , 2007 2007 Citations: 118
Simple Components of the Center of FG / J ( FG ) RA Ferraz Communications in Algebra® 36 (9), 3191-3199 , 2008 2008 Citations: 73
Simple components and central units in group algebras RA Ferraz Journal of Algebra 279 (1), 191-203 , 2004 2004 Citations: 71
Semisimple group codes and dihedral codes FS Dutra, RA Ferraz, CP Milies Algebra and Discrete Mathematics, 28-48 , 2009 2009 Citations: 57
-Equivalence in Group Algebras and Minimal Abelian Codes RA Ferraz, M Guerreiro, CP Milies IEEE Transactions on Information Theory 60 (1), 252-260 , 2013 2013 Citations: 23
Central units in metacyclic integral group rings RA Ferraz, JJ Simón-Pınero Communications in Algebra® 36 (10), 3708-3722 , 2008 2008 Citations: 23
Units of ZCP RA Ferraz Contemporary Mathematics 499, 107 , 2009 2009 Citations: 16
Essential idempotents and simplex codes G Chalom, RA Ferraz, CP Milies Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2 … , 2017 2017 Citations: 15
Some classes of semisimple group (and loop) algebras over finite fields RA Ferraz, EG Goodaire, CP Milies Journal of Algebra 324 (12), 3457-3469 , 2010 2010 Citations: 15
Free Subgroups in the Units of ℤ[ K 8 × C p ] RA Ferraz Communications in Algebra 31 (9), 4291-4299 , 2003 2003 Citations: 11
Units of Z (Cp× C2) and Z (Cp× C2× C2) RA Ferraz, RRM Silva Communications in Algebra 44 (2), 851-872 , 2016 2016 Citations: 8
Minimal Binary Abelian Codes of length G Chalom, RA Ferraz, M Guerreiro, CP Milies arXiv preprint arXiv:1205.5699 , 2012 2012 Citations: 8
Twisted group algebras of Abelian groups A Duarte, RA Ferraz, CP Milies Finite Fields and Their Applications 95, 102386 , 2024 2024 Citations: 7
Units of ℤ C p n RA Ferraz, PM Kitani Communications in Algebra 43 (11), 4936-4950 , 2015 2015 Citations: 6
Minimal codes in binary abelian group algebras M Guerreiro, RA Ferraz, CP Milies 2011 IEEE Information Theory Workshop, 225-228 , 2011 2011 Citations: 5
Central Units in ℤ C p , q RA Ferraz, JJ Simón Communications in Algebra 44 (5), 2264-2275 , 2016 2016 Citations: 4
Essential idempotents in group algebras and coding theory RA Ferraz, CP Milies Indian Journal of Pure and Applied Mathematics 52 (3), 747-760 , 2021 2021 Citations: 3
Left ideals of matrix rings and error-correcting codes RA Ferraz, CP Milies, E Taufer Applicable Algebra in Engineering, Communication and Computing 32, 311-320 , 2021 2021 Citations: 3
Groups generated by a Bass cyclic unit and a bicyclic unit in the units of Z [G]. RA Ferraz Journal of Group Theory 7 (3) , 2004 2004 Citations: 3
Minimal ideals in finite abelian group algebras and coding theory G Chalom, RA Ferraz, M Guerreiro São Paulo Journal of Mathematical Sciences 10 (2), 321-340 , 2016 2016 Citations: 2
