Groups that have the same holomorph as a finite perfect group
نویسندگان
چکیده
منابع مشابه
on finite a-perfect abelian groups
let $g$ be a group and $a=aut(g)$ be the group of automorphisms of $g$. then the element $[g,alpha]=g^{-1}alpha(g)$ is an autocommutator of $gin g$ and $alphain a$. also, the autocommutator subgroup of g is defined to be $k(g)=langle[g,alpha]|gin g, alphain arangle$, which is a characteristic subgroup of $g$ containing the derived subgroup $g'$ of $g$. a group is defined...
متن کاملFinite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
متن کاملSimple groups with the same prime graph as $D_n(q)$
Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...
متن کاملOn some Frobenius groups with the same prime graph as the almost simple group ${ {bf PGL(2,49)}}$
The prime graph of a finite group $G$ is denoted by $Gamma(G)$ whose vertex set is $pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $Gamma(H)=Gamma(G)$, in while $Hnotcong G$. In this paper, we consider finite groups with the same prime gr...
متن کاملOn the Holomorph of a Discrete Group
Abstract. The holomorph of a discrete group G is the universal semi-direct product of G. We construct a resolution for Hol(Zpr ) for every prime p, where Zm denotes a cyclic group of order m, and use it to compute the integer homology and mod p cohomology of Hol(Zpr ) (this computation is long and is omitted here, but will appear in [V]). Also, we study maps of holomorphs of groups and maps of ...
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: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.04.006