on normal automorphisms of n-periodic products of finite cyclic groups
نویسندگان
چکیده
we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.
منابع مشابه
on normal automorphisms of $n$-periodic products of finite cyclic groups
we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.
متن کاملA Note on Absolute Central Automorphisms of Finite $p$-Groups
Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study some properties of absolute central automorphisms of a given finite $p$-group.
متن کاملn-INNER AUTOMORPHISMS OF FINITE GROUPS
We refer to an automorphism g of a group G as n-inner if given any subset S of G with cardinality less than n, there exists an inner automorphism of G agreeing with g on S. Hence g is 2-inner if it sends every element of G to a conjugate. New examples are given of outer n-inner automorphisms of finite groups for all natural numbers n ≥ 2.
متن کاملAutomorphisms of direct products of finite groups II
In this paper we first find the automorphism group of the direct product of n copies of an indecomposable non-abelian group. We describe the automorphism group as matrices with entries which are homomorphisms between the n direct factors. We then use this description with a generalization of a result by Bidwell, Curran, and McCaughan on Aut (H×K), where H and K have no common direct factor, to ...
متن کاملOn equality of absolute central and class preserving automorphisms of finite $p$-groups
Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...
متن کاملClassifying fuzzy normal subgroups of finite groups
In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 2
شماره 3 2012
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023