Nagoya Mathematical Journal

The Schur multipliers of the Mathieu groups

N. Burgoyne and P. Fong

Full-text: Open access

Article information

Source
Nagoya Math. J. Volume 27, Part 2 (1966), 733-745.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1118801786

Mathematical Reviews number (MathSciNet)
MR0197542

Zentralblatt MATH identifier
0171.28801

Subjects
Primary: 20.25

Citation

Burgoyne, N.; Fong, P. The Schur multipliers of the Mathieu groups. Nagoya Math. J. 27 (1966), no. 2, 733--745. http://projecteuclid.org/euclid.nmj/1118801786.


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References

  • [1] E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abhand. Math. Sem. Hamburg, Vol 12 (1938), pp. 256-264.
  • [2] I. Schur, Uber die Darstellung der endlichen Gruppen durch gebrochene lineare Sub- stitutionen, Jour, fur Math. (Crelle), Vol 127 (1904), pp. 20-50 Untersuchungen iiber die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, ibid, Vol 132 (1907), pp. 85-137 Uber die Darstellung der symmetrischen und der alter- nierenden Gruppe durch gebrochene lineare Substitutionen, ibid, Vol 139 (1911), pp. 155-250.
  • [3] G. Frobenius, Uber die Charaktere der mehrfach transitive Gruppen, Sitz. Preuss. Akad. Wissen. (1904), pp. 558-571.
  • [4] D. E. Littlewood, The Theory of Group Characters, 2nd. Ed. Oxford (1950).
  • [5] G. A. Miller, The group of isomorphisms of the simple groups whose degrees are less than 15, Archiv der Math, und Physik, Vol 12 (1907), pp. 249-251 Transitive groups of degree p 2 q1. p and q being prime numbers, Quarterly Jour, of Math. Vol 39 (1908), pp. 210-216.
  • [6] R. Swan, The /-period of a finite group, 111. Jour, of Math. Vol 4 (1960), pp. 341-346.
  • [7] R. Brauer, On groups whose order contains a prime number to the first power I, Amer. Jour. Math. Vol 64 (1942), pp. 401-420.
  • [8] R. G. Stanton, The Mathieu groups, Can. Jour. Math. Vol 3 (1951), pp. 164-174. Tables In Tables 1, 2, 3 the first column describes the conjugacy class by giving its cycle structure in the natural permutation representation of that group. The second column is the order h of the centralizer subgroup of an element in that class. A character written with a bar above it denotes a pair of complex- conjugate characters.Recall that the orders of the Mathieu groups are hn 11.10.9.8, A 12.Aii, fe 22.21.20.48, fes 23.fc, /z24 24.fe. In Table 4 we give the character (see 2 of part II) for the Mn subgroup in Mi2.We only list those classes on which the character is non-zero.In Table 5 we list the values of for f23 in Mu only on those classes for which they are needed in 3 of part II. In Table 6 we only give a single value for the projective character. The other values on each splitting class are multiples of the given value by -g-( - 1U 3).