Finite p-groups of class 3 have noninner automorphisms of order p
نویسندگان
چکیده
منابع مشابه
Finite P-groups of Class 2 Have Noninner Automorphisms of Order P
We prove that for any prime number p, every finite non-abelian p-group G of class 2 has a noninner automorphism of order p leaving either the Frattini subgroup Φ(G) or Ω1(Z(G)) elementwise fixed.
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In this paper we study the longstanding conjecture of whether there exists a noninner automorphism of order p for a finite non-abelian pgroup. Among other results, we prove that if G is a finite non-abelian pgroup, p is odd and G/Z(G) is powerful then G has a noninner automorphism of order p. To prove the latter result we show that the Tate cohomology Hn(G/N, Z(N)) 6= 0 for all n ≥ 0, where G i...
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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 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.
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ژورنال
عنوان ژورنال: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
سال: 2012
ISSN: 0138-4821,2191-0383
DOI: 10.1007/s13366-012-0090-x