Premium
The Symmetric Genus of the Mathieu Groups
Author(s) -
Conder Marston
Publication year - 1991
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/23.5.445
Subject(s) - mathematics , genus , automorphism , symmetric group , combinatorics , group (periodic table) , genus field , pure mathematics , automorphisms of the symmetric and alternating groups , zoology , biology , physics , abelian group , quantum mechanics , abelian extension
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 M 11 , M 12 , M 22 , M 23 and M 24 is determined, with the help of some computer calculations and a little‐known of Ree on permutations.