An addition theorem for finite cyclic groups
نویسندگان
چکیده
منابع مشابه
Olson’s Theorem for Cyclic Groups
Let n be a large number. A subset A of Zn is complete if SA = Zn, where SA is the collection of the subset sums of A. Olson proved that if n is prime and |A| > 2n1/2, then SA is complete. We show that a similar result for the case when n is a composite number, using a different approach.
متن کاملAn Addition Theorem on the Cyclic Group Zpα qβ
Let n > 1 be a positive integer and p be the smallest prime divisor of n. Let S be a sequence of elements from Zn = Z/nZ of length n + k where k ≥ np − 1. If every element of Zn appears in S at most k times, we prove that there must be a subsequence of S of length n whose sum is zero when n has only two distinct prime divisors.
متن کاملFinite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
متن کاملFinite groups all of whose proper centralizers are cyclic
A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic. In this article we determine all finite $CC$-groups.
متن کاملAn Erdős–fuchs Type Theorem for Finite Groups
We establish a finite analogue of the Erdős-Fuchs theorem, showing that the representation function of a non-trivial subset of a finite abelian group cannot be nearly constant. Our results are, essentially, best possible. – Dedicated to Melvyn B. Nathanson and Carl Pomerance on the occasion of their 65th birthday
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00011-8