منابع مشابه
The Symmetric Genus of the Mathieu Groups
The (symmetric) genus of a finite group may be defined as the smallest genus of those closed orientable surfaces on which G acts faithfully as a group of automorphisms. In this paper the genus of each of the five Mathieu groups Mn, M12, M22, M23 and M24 is determined, with the help of some computer calculations and a little-known theorem of Ree on permutations.
متن کاملOn the Genus of Symmetric Groups
A new method for determining genus of a group is described. It involves first getting a bound on the sizes of the generating set for which the corresponding Cayley graph could have smaller genus. The allowable generating sets are then examined by methods of computing average face sizes and by voltage graph techniques to find the best embeddings. This method is used to show that genus of the sym...
متن کاملThe Strong Symmetric Genus of the Hyperoctahedral Groups
In the study of Reimannian manifolds, it is natural to consider the finite groups, which act as automorphisms of the manifold. On the other hand, given a finite group, one may consider the topological surfaces on which the group acts faithfully as a group of automorphisms. There are several natural invariants assigned to a group that are associated to the action of that group on compact orienta...
متن کاملThe Strong Symmetric Genus of the Finite Coxeter Groups
The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving automorphisms. In this paper we complete the calculation of the strong symmetric genus for each finite Coxeter group excluding the group E8.
متن کاملTHE STRONG SYMMETRIC GENUS AND GENERALIZED SYMMETRIC GROUPS OF TYPE G(n, 3)
The generalized symmetric groups are defined to be G(n, m) = Zm o Σn where n, m ∈ Z+. The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving automorphisms. The present work extends work on the strong symmetric genus by Marston Conder, who studied the symmetric groups, which a...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1999
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708959997057x