Virtually-residually-p automorphism groups of group rings
نویسندگان
چکیده
منابع مشابه
AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr
H"{o}lder in 1893 characterized all groups of order $pqr$ where $p>q>r$ are prime numbers. In this paper, by using new presentations of these groups, we compute their full automorphism group.
متن کاملAutomorphism Groups of Schur Rings
In 1993, Muzychuk [18] showed that the rational Schur rings over a cyclic group Zn are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Zn. This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G ...
متن کاملthe automorphism group for $p$-central $p$-groups
a $p$-group $g$ is $p$-central if $g^{p}le z(g)$, and $g$ is $p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin g$. we prove that for $g$ a finite $p^{2}$-abelian $p$-central $p$-group, excluding certain cases, the order of $g$ divides the order of $text{aut}(g)$.
متن کاملthe automorphism group for p-central p-groups
a $p$-group $g$ is $p$-central if $g^{p}le z(g)$, and $g$ is $p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin g$. we prove that for $g$ a finite $p^{2}$-abelian $p$-central $p$-group, excluding certain cases, the order of $g$ divides the order of $text{aut}(g)$.
متن کاملOn the nilpotency class of the automorphism group of some finite p-groups
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: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90103-u