Minimal rank of abelian group matrices

1996 ◽  
Author(s):  
Yip-cheung Chan
Keyword(s):  
Abelian Group ◽  
Minimal Rank ◽  
Group Matrices

Minimal rank of abelian group matrices

1998 ◽  
Vol 44 (3) ◽  
pp. 277-285 ◽  
Author(s):  
Wai-Kiu Chan ◽  
Yip-Cheung Chan ◽  
Man-Keung Siu
Keyword(s):  
Abelian Group ◽  
Minimal Rank ◽  
Group Matrices

scholarly journals Classes of unimodular abelian group matrices

1972 ◽  
Vol 43 (3) ◽  
pp. 633-646 ◽  
Author(s):  
Dennis Garbanati ◽  
Robert Thompson
Keyword(s):  
Abelian Group ◽  
Group Matrices

Determinants of abelian group matrices

1980 ◽  
Vol 9 (2) ◽  
pp. 121-132 ◽  
Author(s):  
Michael K. Mahoney ◽  
Morris Newman
Keyword(s):  
Abelian Group ◽  
Group Matrices

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.

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