منابع مشابه
On solubility of groups with bounded centralizer chains
The c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite cdimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounde...
متن کاملA characterization of simple $K_4$-groups of type $L_2(q)$ and their automorphism groups
In this paper, it is proved that all simple $K_4$-groups of type $L_2(q)$ can be characterized by their maximum element orders together with their orders. Furthermore, the automorphism groups of simple $K_4$-groups of type $L_2(q)$ are also considered.
متن کاملSpin Representations and Centralizer Algebras for the Spinor Groups
We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space ∆ ⊗⊗ k V . Here ∆ is the fundamental representation of Pin(N) and V is the natural (vector) representation of the orthogonal group O(N). We consider the centralizer algebra CPk = EndPin(N)(∆ ⊗⊗k V ) for Pin(N), the double covering group of O(N) and define...
متن کاملOD-characterization of Almost Simple Groups Related to displaystyle D4(4)
Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident...
متن کاملNSE characterization of some linear groups
For a finite group $G$, let $nse(G)={m_kmid kinpi_e(G)}$, where $m_k$ is the number of elements of order $k$ in $G$ and $pi_{e}(G)$ is the set of element orders of $G$. In this paper, we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$, where $min {n,n+1}$ and $2^n-1=p$ is a prime number.
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: Chinese Journal of Mathematics
سال: 2013
ISSN: 2314-8071
DOI: 10.1155/2013/871072