On Finitep-Groups Whose Central Automorphisms are all Class Preserving
نویسندگان
چکیده
منابع مشابه
On 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 کاملFinite groups all of whose proper centralizers are cyclic
A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic. In this article we determine all finite $CC$-groups.
متن کاملClass Preserving Automorphisms of Blackburn Groups
In this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms. 2000 Mathematics subject classification: primary 20D45; secondary 16S34.
متن کاملCLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS
We classify all finite p-groups G for which |Autc(G)| attains its maximum value, where Autc(G) denotes the group of all class preserving automorphisms of G.
متن کاملCLASS-PRESERVING AUTOMORPHISMS OF A FAMILY OF FINITE p-GROUPS
Let G be a finite p-group, p prime such that G has a normal subgroup H , there exists an element y ∈ G, y / ∈ H such that order of y is p, y ∈ ζ(G) and each element g ∈ G can be written as g = h y, h ∈ H, 1 ≤ i ≤ p, where ζ(G) denotes the center of G. It is proved that any τ ∈ Autc(G) such that for all x ∈ H , xτ = (uy)x(uy), where u is a fixed element of H and 1 ≤ i ≤ p is an inner automorphis...
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: Communications in Algebra
سال: 2013
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2012.706347