منابع مشابه
Automorphisms of Finite Abelian Groups
Much less known, however, is that there is a description of Aut(G), the automorphism group of G. The first compete characterization that we are aware of is contained in a paper by Ranum [1] near the turn of the last century. Beyond this, however, there are few other expositions. Our goal is to fill this gap, thereby providing a much needed accessible and modern treatment. Our characterization o...
متن کاملOn Involutive Anti-Automorphisms of Finite Abelian Groups
We investigate various aspects of involutions of groups, i.e, anti-automorphisms of order at most two. The emphasis is on finite abelian groups. We count the number of involutions for the cyclic groups, and consider the problem for direct products of groups. We also give a characterization for the set of skewed squares of finitely generated abelian groups with identity as the involution. The pr...
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 کاملInverse Correspondences in Automorphisms of Abelian Groups
The totality of the operators which correspond to their inverses in an automorphism of an abelian group G obviously constitutes a subgroup of G. I t is well known that G cannot contain any characteristic operator besides the identity unless this operator is of order 2, and that it cannot contain more than one characteristic operator of this order. Hence it results that whenever G contains any c...
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...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2007
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2007.11920485