Minimal ideals in finite abelian group algebras and coding theory

2016 ◽  
Vol 10 (2) ◽  
pp. 321-340
Author(s):  
Gladys Chalom ◽  
Raul Antonio Ferraz ◽  
Marinês Guerreiro
Keyword(s):  
Abelian Group ◽  
Coding Theory ◽  
Finite Abelian Group ◽  
Group Algebras

Zeros of Functions in Finite Abelian Group Algebras

1976 ◽  
Vol 98 (1) ◽  
pp. 197 ◽  
Author(s):  
Philippe Delsarte ◽  
Robert J. McEliece
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Group Algebras ◽  
Zeros Of Functions

A note on Lie nilpotent group algebras

2019 ◽  
Vol 18 (09) ◽  
pp. 1950163
Author(s):  
Meena Sahai ◽  
Bhagwat Sharan
Keyword(s):  
Abelian Group ◽  
Nilpotent Group ◽  
Group Algebra ◽  
Upper Bound ◽  
Finite Abelian Group ◽  
Index Formula ◽  
Group Algebras ◽  
Arbitrary Group ◽  
Nilpotency Index

Let [Formula: see text] be an arbitrary group and let [Formula: see text] be a field of characteristic [Formula: see text]. In this paper, we give some improvements of the upper bound of the lower Lie nilpotency index [Formula: see text] of the group algebra [Formula: see text]. We also give improved bounds for [Formula: see text], where [Formula: see text] is the number of independent generators of the finite abelian group [Formula: see text]. Furthermore, we give a description of the Lie nilpotent group algebra [Formula: see text] with [Formula: see text] or [Formula: see text]. We also show that for [Formula: see text] and [Formula: see text], [Formula: see text] if and only if [Formula: see text], where [Formula: see text] is the upper Lie nilpotency index of [Formula: see text].

Generalized Commutativity in Group Algebras

2003 ◽  
Vol 46 (1) ◽  
pp. 14-25 ◽  
Author(s):  
Yu. A. Bahturin ◽  
M. M. Parmenter
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Group Algebras ◽  
Study Group

AbstractWe study group algebras FG which can be graded by a finite abelian group Γ such that FG is β-commutative for a skew-symmetric bicharacter β on Γ with values in F*.

scholarly journals K2 of finite abelian group algebras

2009 ◽  
Vol 213 (7) ◽  
pp. 1201-1207 ◽  
Author(s):  
Yubin Gao ◽  
Guoping Tang
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Group Algebras

Some remarks on K2 and K3 of finite abelian group algebras

2019 ◽  
Vol 18 (05) ◽  
pp. 1950094
Author(s):  
Hao Zhang ◽  
Guoping Tang ◽  
Hang Liu
Keyword(s):  
Abelian Group ◽  
Finite Field ◽  
Group Structure ◽  
Finite Abelian Group ◽  
Group Algebras

Let [Formula: see text] be a finite abelian [Formula: see text]-group and [Formula: see text] a finite field of characteristic [Formula: see text]. We give an algorithm to write down a set of generators of [Formula: see text] via a simple presentation of it and obtain some formulae for counting these generators. Using Witt decomposition, we also determine the group structure of [Formula: see text].

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

Representation of zero-sum invariants by sets of zero-sum sequences over a finite abelian group

2021 ◽  
Author(s):  
Weidong Gao ◽  
Siao Hong ◽  
Wanzhen Hui ◽  
Xue Li ◽  
Qiuyu Yin ◽  
...  
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Zero Sum
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