scholarly journals From uncountable abelian groups to uncountable nonabelian groups

2020 ◽  
Vol 144 ◽  
pp. 105-114
Author(s):  
Katsuya Eda
Keyword(s):  
Abelian Groups ◽  
Nonabelian Groups

scholarly journals On lacunary sets for nonabelian groups

1978 ◽  
Vol 25 (2) ◽  
pp. 167-176 ◽  
Author(s):  
A. H. Dooley
Keyword(s):  
Necessary Conditions ◽  
Abelian Groups ◽  
Sidon Sets ◽  
Compact Abelian Groups ◽  
Nonabelian Groups

AbstractResults concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards and Ross. A notion of test family is introduced and is used to give necessary conditions for a set to be lacunary. Using this, it is shown that (2) has no infinite p-Sidon sets for 1 ≤p<2.

Adding Distinct Congruence Classes

1998 ◽  
Vol 7 (1) ◽  
pp. 81-87 ◽  
Author(s):  
Y. O. HAMIDOUNE
Keyword(s):  
Cyclic Group ◽  
Abelian Groups ◽  
Congruence Classes ◽  
Nonabelian Groups

Let S be a generating subset of a cyclic group G such that 0=∉S and [mid ]S[mid ][ges ]5. We show that the number of sums of the subsets of S is at least min([mid ]G[mid ], 2[mid ]S[mid ]). Our bound is best possible. We obtain similar results for abelian groups and mention the generalization to nonabelian groups.

scholarly journals Adders for the patterned starter in nonabelian groups

1976 ◽  
Vol 21 (2) ◽  
pp. 185-193 ◽  
Author(s):  
Kenneth B. Gross ◽  
Philip A. Leonard
Keyword(s):  
Large Class ◽  
Abelian Groups ◽  
Odd Order ◽  
Room Squares ◽  
Combinatorial Constructions ◽  
Nonabelian Groups

AbstractStarters with adders, in abelian groups of odd order, have been used widely in recent combinatorial constructions, most notably in the study of Room squares. In this paper, constructions of adders for the so-called “patterned starter” are described, for a large class of nonabelian groups of odd order.

scholarly journals Enumeration of (16,4,16,4) Relative Difference Sets

10.37236/2776 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
David Clark ◽  
Vladimir D. Tonchev
Keyword(s):  
Normal Subgroup ◽  
Abelian Groups ◽  
Difference Sets ◽  
Relative Difference ◽  
Complete Enumeration ◽  
Relative Difference Sets ◽  
Nonabelian Groups

A complete enumeration of relative difference sets (RDS) with parameters $(16,4,16,4)$ in a group of order 64 with a normal subgroup $N$ of order 4 is given. If $N=Z_4$, three of the 11 abelian groups of order 64, and 23 of the 256 nonabelian groups of order 64 contain  $(16,4,16,4)$ RDSs. If $N=Z_2 \times Z_2$, nine of the abelian groups and 194 of the non-abelian groups of order 64 contain  $(16,4,16,4)$  RDSs.

scholarly journals Bounds for Matchings in Nonabelian Groups

10.37236/7520 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Will Sawin
Keyword(s):  
Finite Group ◽  
Perfect Matching ◽  
Abelian Groups ◽  
Upper Bounds ◽  
Exponential Bounds ◽  
Arbitrary Finite Group ◽  
A Finite Group ◽  
Nonabelian Groups

We give upper bounds for triples of subsets of a finite group such that the triples of elements that multiply to $1$ form a perfect matching. Our bounds are the first to give exponential savings in powers of an arbitrary finite group. Previously, Blasiak, Church, Cohn, Grochow, Naslund, Sawin, and Umans (2017) gave similar bounds in abelian groups of bounded exponent, and Petrov (2016) gave exponential bounds in certain $p$-groups. 

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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