The Schur Multipliers of the Mathieu Groups
- 1 July 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 27 (2) , 733-745
- https://doi.org/10.1017/s0027763000026519
Abstract
The Mathieu groups are the finite simple groups M11, M12, M22, M23, M24 given originally as permutation groups on respectively 11, 12, 22, 23, 24 symbols. Their definition can best be found in the work of Witt [1]. Using a concept from Lie group theory we can describe the Schur multiplier of a group as the center of a “simply-connected” covering of that group. A precise definition will be given later. We also mention that the Schur multiplier of a group is the second cohomology group of that group acting trivially on the complex roots of unity. The purpose of this paper is to determine the Schur multipliers of the five Mathieu groups.Keywords
This publication has 3 references indexed in Scilit:
- The Mathieu GroupsCanadian Journal of Mathematics, 1951
- On Groups Whose Order Contains a Prime Number to the First Power IAmerican Journal of Mathematics, 1942
- Die 5-fach transitiven gruppen von mathieuAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1937