Finite soluble groups have large centralisers
نویسندگان
چکیده
منابع مشابه
CENTRALISERS OF FINITE SUBGROUPS IN SOLUBLE GROUPS OF TYPE FPn
We show that for soluble groups of type FPn, centralisers of finite subgroups need not be of type FPn.
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 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 کاملCentralisers of Involutions in Black Box Groups
We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the p-core of a black box group of odd characteristic. This special role of involutions suggest that the theory of black box groups reproduces, at a non-determi...
متن کاملConstructing Normalisers in Finite Soluble Groups
This paper describes algorithms for constructing a Hall n-subgroup H of a finite soluble group G and the normaliser No(H). If G has composition length n, then H and No(H ) can be constructed using O(n ~ log IGI) and O(n ~ log IGI) group multiplications, respectively. These algorithms may be used to construct other important subgroups such as Carter subgroups, system normalisers and relative sys...
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: Bulletin of the Australian Mathematical Society
سال: 1987
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700013241