On a Permutation Problem for Finite Abelian Groups
نویسندگان
چکیده
منابع مشابه
On a Permutation Problem for Finite Abelian Groups
LetG be a finite additive abelian group with exponent n > 1, and let a1, . . . , an−1 be elements of G. We show that there is a permutation σ ∈ Sn−1 such that all the elements saσ(s) (s = 1, . . . , n− 1) are nonzero if and only if ∣∣∣{1 6 s < n : n d as 6= 0 }∣∣∣ > d− 1 for every positive divisor d of n. When G is the cyclic group Z/nZ, this confirms a conjecture of Z.-W. Sun.
متن کاملA Problem of Wielandt on Finite Permutation Groups
Problem 6.6 in the Kourovka Notebook [9], posed by H. Wielandt, reads as follows. ' Let P, Q be permutation representations of a finite group G with the same character. Suppose P(G) is a primitive permutation group. Is Q{G) necessarily primitive? Equivalently: Let A, B be subgroups of a finite group G such that for each class C of conjugate elements of G their intersection with C has the same c...
متن کاملon finite a-perfect abelian groups
let $g$ be a group and $a=aut(g)$ be the group of automorphisms of $g$. then the element $[g,alpha]=g^{-1}alpha(g)$ is an autocommutator of $gin g$ and $alphain a$. also, the autocommutator subgroup of g is defined to be $k(g)=langle[g,alpha]|gin g, alphain arangle$, which is a characteristic subgroup of $g$ containing the derived subgroup $g'$ of $g$. a group is defined...
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 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: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5915