On the automorphism group of the p-adic group ring of a metacyclic p-group
نویسندگان
چکیده
منابع مشابه
ON THE STRUCTURE OF THE AUTOMORPHISM GROUP OF A MINIMAL NONABELIAN p-GROUP (METACYCLIC CASE)
In this paper we find the complete structure for the automorphism groups of metacyclic minimal nonabelian 2-groups. This, together with [6, 7], gives the complete answer to the Question 15 from [5] (respectively Question 20 from [4]) in the case of metacyclic groups. We also correct some inaccuracies and extend the results from [13].
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The Dade group D(P ) of a finite p-group P , formed by equivalence classes of endopermutation modules, is a finitely generated abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of P and it is conjectured that every nontrivial element of its torsion subgroup D(P ) has order 2, (or also 4, in case p = 2). The group D(P ) is closely related to the ...
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Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1983
ISSN: 0021-8693
DOI: 10.1016/0021-8693(83)90162-x