Antiautomorphisms and Biantiautomorphisms of Some Finite Abelian Groups
نویسندگان
چکیده
منابع مشابه
Finite $p$-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 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 کاملSome Observations regarding the Holomorphs of Finite Abelian Groups
Presentations for the holomorphs of abelian groups of the form Cpn × 1 for p=2 or an odd prime are given. These presentations extend the results given in Burnside’s well-known text on finite groups on the holomorphs for the cyclic groups of orders p for p being an odd or even prime. The following set of observations all deal with the holomorphs of finite abelian groups. The motivation here is t...
متن کاملSome Remarks on the Logarithmic Signatures of Finite Abelian Groups
In the paper about the cryptosystem MST3, Svaba and Trung proposed a way to build a cryptosystem based on the concept of logarithmic signatures, and they choose Suzuki’s group, which is not abelian for implementing. Recently, to reason why these methods cannot be applied to abelian groups; Svaba, Trung and Wolf developed some algorithms to factorize the fused transversal logarithmic signatures ...
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: Symmetry
سال: 2020
ISSN: 2073-8994
DOI: 10.3390/sym12020294