Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups

2021 ◽  
Vol 314 (1) ◽  
pp. 138-143
Author(s):  
Máté Matolcsi ◽  
Imre Z. Ruzsa
Keyword(s):  
Exponential Sums ◽  
Difference Sets ◽  
Cyclic Groups

scholarly journals Nonexistence of certain supplementary difference sets

1975 ◽  
Vol 13 (3) ◽  
pp. 343-348 ◽  
Author(s):  
Nicholas Wormald
Keyword(s):  
Difference Sets ◽  
Cyclic Groups ◽  
Supplementary Difference Sets ◽  
Supplementary Difference ◽  
Index 2

This paper finds restrictions on the parameters of supplementary difference sets in any group G with a subgroup of index 2, which therefore includes all cyclic groups of even orders. As a corollary to the main theorem, we have that if S1, …, Sr are r − {2v, k1, …, kr; 2λ} supplementary difference sets in such a group, then not all of v, k1, …, kr, λ are odd; also is the sum of r squares.

scholarly journals Inequivalence of Difference Sets: On a Remark of Baumert

10.37236/2277 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Padraig Ó Catháin
Keyword(s):  
Difference Sets ◽  
Cyclic Groups ◽  
Cyclic Difference Sets

An often cited statement of Baumert in his book Cyclic difference sets asserts that four well known families of cyclic $(4t-1,2t-1,t-1)$ difference sets are inequivalent, apart from a small number of exceptions with $t< 8$. We are not aware of a proof of this statement in the literature.Three of the families discussed by Baumert have analogous constructions in non-cyclic groups. We extend his inequivalence statement to a general inequivalence result, for which we provide a complete and self-contained proof. We preface our proof with a survey of the four families of difference sets, since there seems to be some confusion in the literature between the cyclic and non-cyclic cases.

On the minimal varieties of PI-algebras graded by finite cyclic groups

2021 ◽  
pp. 1-25
Author(s):  
Marcos Antônio da Silva Pinto ◽  
Viviane Ribeiro Tomaz da Silva
Keyword(s):  
Cyclic Groups
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