منابع مشابه
Genus Spectra for Split Metacyclic Groups
An integer n ! 2 is said to be a genus of a finite group G if there is a compact Riemann surface of genus n on which G acts as a group of automorphisms. In this paper, formulae are given for the minimum genus, minimum stable genus and the gap sequence, i.e., the (finite) set of non-genera, for a split metacyclic group of order pq, where p and q are primes. This information completely determines...
متن کاملThe non-orientable genus of some metacyclic groups
In the case of a 2-cell embedding (i.e., in the case where every region of the embedding is homeomorphic to a disk), the'inequality can easily be derived from the Euler Formula, v e + f = 2 2"fwhere e is the number of edges and f is the number of 2-cells of the embedding): the Handshaking Lemma asserts 2e = dv, and applying the Handshaking Lemma to the dual graph yields 2e >. gf; incorporating ...
متن کاملThe 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 کاملCharacter Tables of Metacyclic Groups
We show that two metacyclic groups of the following types are isomorphic if they have the same character tables: (i) split metacyclic groups, (ii) the metacyclic p-groups and (iii) the metacyclic {p, q}-groups, where p, q are odd primes. 2010 Mathematics Subject Classification. Primary 20C15; Secondary 20D15, 20F16, 20F22.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1995
ISSN: 0166-8641
DOI: 10.1016/0166-8641(95)00028-f