Zero-inducing functions on finite abelian groups
نویسندگان
چکیده
منابع مشابه
Two zero-sum invariants on finite abelian groups
Let G be an additive finite abelian group with exponent exp(G). Let s(G) (resp. η(G)) be the smallest integer t such that every sequence of t elements (repetition allowed) from G contains a zero-sum subsequence T of length |T | = exp(G) (resp. |T | ∈ [1, exp(G)]). Let H be an arbitrary finite abelian group with exp(H) = m. In this paper, we show that s(Cmn ⊕ H) = η(Cmn ⊕ H) + mn − 1 holds for a...
متن کاملOn Zero-sum Subsequences in Finite Abelian Groups
Let G be a finite abelian group and k ∈ N with k exp(G). Then Ek(G) denotes the smallest integer l ∈ N such that every sequence S ∈ F(G) with |S| ≥ l has a zero-sum subsequence T with k |T |. In this paper we prove that if G = Cn1 ⊕ · · · ⊕ Cnr is a p-group, k ∈ N with k exp(G) and gcd(p, k) = 1, then Ek(G) = ⌊ k k − 1 r ∑
متن کاملOn non-normal non-abelian subgroups of finite groups
In this paper we prove that a finite group $G$ having at most three conjugacy classes of non-normal non-abelian proper subgroups is always solvable except for $Gcong{rm{A_5}}$, which extends Theorem 3.3 in [Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable, Acta Math. Sinica (English Series) 27 (2011) 891--896.]. Moreover, we s...
متن کاملOn $m^{th}$-autocommutator subgroup of finite abelian groups
Let $G$ be a group and $Aut(G)$ be the group of automorphisms of $G$. For any natural number $m$, the $m^{th}$-autocommutator subgroup of $G$ is defined as: $$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G,alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$ In this paper, we obtain the $m^{th}$-autocommutator subgroup of all finite abelian groups.
متن کاملInverse zero-sum problems in finite Abelian p-groups
— In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, the method that we use here enables us to show that, if we ...
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: Pacific Journal of Mathematics
سال: 1982
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1982.98.381