Automorphism groups retracting onto symmetric groups
نویسندگان
چکیده
منابع مشابه
On minimal symmetric automorphism groups of finite symmetric graphs
Let r be finite connected and G a group of automorphisms of r which is transitive on vertices. Suppose that, for a vertex 0 of r, S ~ G~(O') ::; Aut S for some simple group S with S acting primitively on the set r( a) of neighbours of 0, and suppose that G is minimal with these properties. Then one of: (i) G is a nonabelian simple group, (ii) r is a Cayley graph for a normal subgroup N of G and...
متن کاملAUTOMORPHISM GROUPS OF SOME NON-TRANSITIVE GRAPHS
An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...
متن کاملAUTOMORPHISM 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 کاملOn Outer Automorphism Groups of Coxeter Groups
It is shown that the outer automorphism group of a Coxeter group W of nite rank is nite if the Coxeter graph contains no innnite bonds. A key step in the proof is to show that if the group is irreducible and 1 and 2 any two bases of the root system of W, then 2 = w 1 for some w 2 W. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Bri...
متن کاملOuter Automorphism Groups of Bieberbach Groups
Let Γ be a Bieberbach group it is a fundamental group of a flat manifold. In this paper we give necessary and sufficient conditions on Out(Γ) to be infinite. We also compare our result with the previous one ([8], Theorem 7.1) about Anosov automorphisms of flat manifolds. We give several examples of Bieberbach groups.
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: Pacific Journal of Mathematics
سال: 1979
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1979.81.93